BspCrvDeriveRational

(symb_lib/bsp_sym.c:364)

Prototype:

  CagdCrvStruct *BspCrvDeriveRational(CagdCrvStruct *Crv)


Description:

Given a rational Bspline curve - computes its derivative curve (Hodograph) using the quotient rule for differentiation.

Parameters:

Crv: Bspline curve to differentiate.


Returned Value:

CagdCrvStruct *: Differentiated rational Bspline curve.


See Also:

BzrCrvDerive BspCrvDerive BzrCrvDeriveRational CagdCrvDerive

Keywords:

derivatives

BspCrvMult

(symb_lib/bsp_sym.c:58)

Prototype:

  CagdCrvStruct *BspCrvMult(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two Bspline curves - multiply them coordinatewise. The two curves are promoted to same point type before the multiplication can take place. See also BspMultInterpFlag.

Parameters:

Crv1, Crv2: The two curves to multiply.


Returned Value:

CagdCrvStruct *: The product Crv1 * Crv2 coordinatewise.


Keywords:

product

BspMultInterpFlag

(symb_lib/bsp_sym.c:34)

Prototype:

  int BspMultInterpFlag(int BspMultUsingInter)


Description:

Sets method of Bspline product computation.

Parameters:

BspMultUsingInter: If TRUE, Bspline product iscomputed by setting an interpolation problem. Otherwise, by decomposing the Bspline geometry to Bezier geometry.


Returned Value:

int: Previous setting.


Keywords:

product

BspSrfDeriveRational

(symb_lib/bsp_sym.c:461)

Prototype:

  CagdSrfStruct *BspSrfDeriveRational(CagdSrfStruct *Srf, CagdSrfDirType Dir)


Description:

Given a rational Bspline surface - computes its derivative surface in direction Dir, using the quotient rule for differentiation.

Parameters:

Srf: Bspline surface to differentiate.
Dir: Direction of Differentiation. Either U or V.


Returned Value:

CagdSrfStruct *: Differentiated rational Bspline surface.


See Also:

CagdSrfDerive BzrSrfDerive BspSrfDerive BzrSrfDeriveRational

Keywords:

derivatives

BspSrfMult

(symb_lib/bsp_sym.c:223)

Prototype:

  CagdSrfStruct *BspSrfMult(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two Bspline surfaces - multiply them coordinatewise. The two surfaces are promoted to same point type before multiplication can take place. See also BspMultInterpFlag.

Parameters:

Srf1, Srf2: The two surfaces to multiply.


Returned Value:

CagdSrfStruct *: The product Srf1 * Srf2 coordinatewise.


Keywords:

product

BzrApproxBzrCrvAsCubicPoly

(symb_lib/bzr_sym.c:490)

Prototype:

  CagdCrvStruct *BzrApproxBzrCrvAsCubicPoly(CagdCrvStruct *Crv, CagdRType Tol2)


Description:

Given a Bezier curve with order larger than cubic, approximate it using piecewise cubic curves. A C^1 continuous approximation is computed so that the approximation is at most sqrt(Tol2) away from the given curve. Input curve can be rational, although output is always polynomial.

Parameters:

Crv: To approximate using cubic Bezier curves.
Tol2: Accuracy control.


Returned Value:

CagdCrvStruct *: List of cubic Bezier curves approximating Crv.


Keywords:

approximation conversion

BzrApproxBzrCrvAsCubics

(symb_lib/bzr_sym.c:415)

Prototype:

  CagdCrvStruct *BzrApproxBzrCrvAsCubics(CagdCrvStruct *Crv,
                                         CagdRType Tol,
                                         CagdRType MaxLen,
                                         CagdBType NoRational)


Description:

Given a Bezier curve - convert it to (possibly) piecewise cubic. If the curve is 1. A cubic - a copy if it is returned. 2. Lower than cubic - a degree raised (to a cubic) curve is returned. 3. Higher than cubic - a C^1 continuous piecewise cubic approximation is computed for Crv. In case 3 a list of polynomial cubic curves is returned. Tol is then used for the distance tolerance error measure for the approximation. If, however, NoRational is set, rational curves of any order will also be approximated using cubic polynomials. Furthermore if the total length of control polygon is more than MaxLen, the curve is subdivided until this is not the case.

Parameters:

Crv: To approximate using cubic Bezier polynomials.
Tol: Accuracy control.
MaxLen: Maximum arc length of curve.
NoRational: Do we want to approximate rational curves as well?


Returned Value:

CagdCrvStruct *: A list of cubic Bezier polynomials approximating Crv.


Keywords:

conversion approximation

BzrComposeCrvCrv

(symb_lib/composit.c:282)

Prototype:

  CagdCrvStruct *BzrComposeCrvCrv(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two Bezier curves, Crv1 and Crv2, computes their composition Crv1(Crv2(t)). Crv2 must be a scalar curve completely contained in Crv1's parametric domain. See: "Freeform surfcae analysis using a hybrid of symbolic and numeric computation" by Gershon Elber, PhD thesis, University of Utah, 1992.

Parameters:

Crv1, Crv2: The two curve to compose together.


Returned Value:

CagdCrvStruct *: The composed curve.


Keywords:

composition

BzrComposeSrfCrv

(symb_lib/composit.c:478)

Prototype:

  CagdCrvStruct *BzrComposeSrfCrv(CagdSrfStruct *Srf, CagdCrvStruct *Crv)


Description:

Given a Bezier curve Crv and a Bezier surface Srf, computes their coomposition Srf(Crv(t)). Crv must be a two dimensional curve completely contained in the parametric domain of Srf. See: "Freeform surfcae analysis using a hybrid of symbolic and numeric computation" by Gershon Elber, PhD thesis, University of Utah, 1992.

Parameters:

Srf, Crv: The curve and surface to compose.


Returned Value:

CagdCrvStruct *: The resulting composition.


Keywords:

composition

BzrCrvDeriveRational

(symb_lib/bzr_sym.c:214)

Prototype:

  CagdCrvStruct *BzrCrvDeriveRational(CagdCrvStruct *Crv)


Description:

Given a rational Bezier curve - computes its derivative curve (Hodograph) using the quotient rule for differentiation.

Parameters:

Crv: Bezier curve to differentiate.


Returned Value:

CagdCrvStruct *: Differentiated rational Bezier curve.


See Also:

BzrCrvDerive BspCrvDerive BspCrvDeriveRational CagdCrvDerive

Keywords:

derivatives

BzrCrvMult

(symb_lib/bzr_sym.c:26)

Prototype:

  CagdCrvStruct *BzrCrvMult(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two Bezier curves - multiply them coordinatewise. The two curves are promoted to same point type before the multiplication can take place.

Parameters:

Crv1, Crv2: The two curves to multiply.


Returned Value:

CagdCrvStruct *: The product Crv1 * Crv2 coordinatewise.


Keywords:

product

BzrCrvMultList

(symb_lib/bzr_sym.c:90)

Prototype:

  CagdCrvStruct *BzrCrvMultList(CagdCrvStruct *Crv1Lst, CagdCrvStruct *Crv2Lst)


Description:

Given two Bezier curve lists - multiply them one at a time. Return a Bezier curve lists representing their products.

Parameters:

Crv1Lst: First list of Bezier curves to multiply.
Crv2Lst: Second list of Bezier curves to multiply.


Returned Value:

CagdCrvStruct *: A list of product curves


Keywords:

product

BzrSrfDeriveRational

(symb_lib/bzr_sym.c:309)

Prototype:

  CagdSrfStruct *BzrSrfDeriveRational(CagdSrfStruct *Srf, CagdSrfDirType Dir)


Description:

Given a rational Bezier surface - computes its derivative surface in direction Dir, using the quotient rule for differentiation.

Parameters:

Srf: Bezier surface to differentiate.
Dir: Direction of Differentiation. Either U or V.


Returned Value:

CagdSrfStruct *: Differentiated rational Bezier surface.


See Also:

CagdSrfDerive BzrSrfDerive BspSrfDerive BspSrfDeriveRational

Keywords:

derivatives

BzrSrfMult

(symb_lib/bzr_sym.c:128)

Prototype:

  CagdSrfStruct *BzrSrfMult(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two Bezier surfaces - multiply them coordinatewise. The two surfaces are promoted to same point type before multiplication can take place.

Parameters:

Srf1, Srf2: The two surfaces to multiply.


Returned Value:

CagdSrfStruct *: The product Srf1 * Srf2 coordinatewise.


Keywords:

product

SymbAdapIsoExtract

(symb_lib/adap_iso.c:103)

Prototype:

  CagdCrvStruct *SymbAdapIsoExtract(CagdSrfStruct *Srf,
                                    CagdSrfStruct *NSrf,
                                    SymbAdapIsoDistSqrFuncType AdapIsoDistFunc,
                                    CagdSrfDirType Dir,
                                    CagdRType Eps,
                                    CagdBType FullIso,
                                    CagdBType SinglePath)


Description:

Extracts a valid coverage set of isolines from the given surface in the given direction and epsilon. If FullIso is TRUE, all extracted isocurves are spanning the entire parametric domain. If SinglePath is TRUE, the entire coverage is going to be a single curve. If NSrf != NULL, every second curve will be a vector field curve representing the unnormalized normal for the previous Euclidean curve. This mode disable the SinglePath mode. See also function SymbSetAdapIsoExtractMinLevel.

Parameters:

Srf: To compute adaptive isocurve coverage form
NSrf: Normal vector field defining the normals of Srf.
AdapIsoDistFunc: ptional function to invoke with the two adjacent isoparametric curves of the coverage to evaluate the distance between them.
Dir: Direction of adaptive isocurve extraction. Either U or V.
Eps: Tolerance of adaptive isocurve cuverage. For every point P on Srf there will be a point Q in one of the extracted isocurves such the |P - Q| < Eps.
FullIso: Do we want all isocurves to span the entire domain?
SinglePath: o we want a single curve through them all?


Returned Value:

CagdCrvStruct *: A list of curves representing the computed adaptive isocurve coverage for surface Srf. If normal field, NSrf, is prescribed, normal curves are concatenated alternatingly in this list.


Keywords:

adaptive isocurves

SymbAllPrisaSrfs

(symb_lib/prisa.c:54)

Prototype:

  CagdSrfStruct *SymbAllPrisaSrfs(CagdSrfStruct *Srfs,
                                  int SamplesPerCurve,
                                  CagdRType Epsilon,
                                  CagdSrfDirType Dir,
                                  CagdVType Space)


Description:

Computes a piecewise ruled surface approximation to a given set of surfaces with given Epsilon, and lay them out "nicely" onto the XY plane, by approximating each ruled surface as a developable surface with SamplesPerCurve samples. Dir controls the direction of ruled approximation, SpaceScale and Offset controls the placement of the different planar pieces. Prisa is the hebrew word for the process of flattening out a three dimensional surface. I have still to find an english word for it.

Parameters:

Srfs: To approximate and faltten out.
SamplesPerCurve: uring the approximation of a ruled surface as a developable surface.
Epsilon: Accuracy control for the piecewise ruled surface approximation.
Dir: Direction of ruled/developable surface approximation. Either U or V.
Space: A vector in the XY plane to denote the amount of translation from one flattened out surface to the next.


Returned Value:

CagdSrfStruct *: A list of planar surfaces denoting the layout (prisa) of the given Srfs to the accuracy requested.


Keywords:

layout prisa

SymbComposeCrvCrv

(symb_lib/composit.c:37)

Prototype:

  CagdCrvStruct *SymbComposeCrvCrv(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves, Crv1 and Crv2, computes the composition Crv1(Crv2(t)). Crv2 must be a scalar curve completely contained in Crv1's parametric domain.

Parameters:

Crv1, Crv2: The two curve to compose together.


Returned Value:

CagdCrvStruct *: The composed curve.


Keywords:

composition

SymbComposeSrfCrv

(symb_lib/composit.c:365)

Prototype:

  CagdCrvStruct *SymbComposeSrfCrv(CagdSrfStruct *Srf, CagdCrvStruct *Crv)


Description:

Given a curve Crv and surface Srf, computes the composition Srf(Crv(t)). Crv must be a two dimensional curve completely contained in the parametric domain of Srf.

Parameters:

Srf, Crv: The curve and surface to compose.


Returned Value:

CagdCrvStruct *: The resulting composition.


Keywords:

composition

SymbCrv2DCurvatureSign

(symb_lib/curvatur.c:351)

Prototype:

  CagdCrvStruct *SymbCrv2DCurvatureSign(CagdCrvStruct *Crv)


Description:

Computes a scalar curve representing the curvature sign of a planar curve. The given curve is assumed to be planar and only its x and y coordinates are considered. Then the curvature sign is equal to 
     .  ..    .  ..
s =  X  Y  -  Y  X


Parameters:



 Crv:  




Returned Value:



  CagdCrvStruct *:




See Also:

  SymbCrv2DCurvatureSqr
  SymbCrv3DCurvatureSqr
  SymbCrv3DCurvatureSqr
  
  SymbCrv3DRadiusNormal
  SymbCrv3DCurvatureNormal
  SymbCrv2DInflectionPts
  
  SymbCrv2DExtremCrvtrPts


Keywords:

  curvature


 SymbCrv2DCurvatureSqr 
  (symb_lib/curvatur.c:41)

Prototype:

  CagdCrvStruct *SymbCrv2DCurvatureSqr(CagdCrvStruct *Crv)



Description:


Computes a scalar curve representing the curvature of a planar curve. The given curve is assumed to be planar and only its x and y coordinates are considered. Then the curvature k is equal to 
     .  ..    .  ..
     X  Y  -  Y  X
k =  -------------
        .2   .2  3/2
     (  X  + Y  )

Since we cannot represent k because of the square root, we compute and represent k^2.

Parameters:

Crv: To compute the square of teh curvature field for.


Returned Value:

CagdCrvStruct *: The square of the curvature field of Crv.


See Also:

SymbCrv3DCurvatureSqr SymbCrv3DRadiusNormal SymbCrv3DCurvatureNormal SymbCrv2DCurvatureSign SymbCrv2DInflectionPts SymbCrv2DExtremCrvtrPts

Keywords:

curvature

SymbCrv2DExtremCrvtrPts

(symb_lib/curvatur.c:519)

Prototype:

  CagdPtStruct *SymbCrv2DExtremCrvtrPts(CagdCrvStruct *Crv, CagdRType Epsilon)


Description:

Given a planar curve, finds all its extreme curvatrue points by finding the set of extreme locations on the curvature function of Crv.

Parameters:

Crv: To find all int extrem curvature locations.
Epsilon: Accuracy control.


Returned Value:

CagdPtStruct *: A list of parameter values on Crv that have extrem curvature values.


See Also:

SymbCrv2DCurvatureSqr SymbCrv3DCurvatureSqr SymbCrv3DCurvatureSqr SymbCrv3DRadiusNormal SymbCrv3DCurvatureNormal SymbCrv2DCurvatureSign SymbCrv2DInflectionPts

Keywords:

curvature

SymbCrv2DInflectionPts

(symb_lib/curvatur.c:486)

Prototype:

  CagdPtStruct *SymbCrv2DInflectionPts(CagdCrvStruct *Crv, CagdRType Epsilon)


Description:

Given a planar curve, finds all its inflection points by finding the zero set of the sign of the curvature function of the curve.

Parameters:

Crv: To find all its inflection points.
Epsilon: Accuracy control.


Returned Value:

CagdPtStruct *: A list of parameter values on Crv that are inflection points.


See Also:

SymbCrv2DCurvatureSqr SymbCrv3DCurvatureSqr SymbCrv3DCurvatureSqr SymbCrv3DRadiusNormal SymbCrv3DCurvatureNormal SymbCrv2DCurvatureSign SymbCrv2DExtremCrvtrPts

Keywords:

curvature inflection points

SymbCrv2Polyline

(symb_lib/symbpoly.c:208)

Prototype:

  CagdPolylineStruct *SymbCrv2Polyline(CagdCrvStruct *Crv,
                                       int SamplesPerCurve,
                                       CagdBType Optimal,
                                       CagdBType OptiLin)


Description:

Routine to approx. a single curve as a polyline with SamplesPerCurve samples. Polyline is always E3 CagdPolylineStruct type. NULL is returned in case of an error, otherwise CagdPolylineStruct.

Parameters:

Crv: To approximate as a polyline.
SamplesPerCurve: Number of samples to approximate with.
Optimal: If TRUE, yse optimal approximation of isocurves. Otherwise, the curve is sampled using equally spaced samples in parametric space.
OptiLin: If TRUE, optimize linear curves.


Returned Value:

CagdPolylineStruct *: A polyline representing the piecewise linear approximation from, or NULL in case of an error.


See Also:

BspCrv2Polyline BzrCrv2Polyline IritCurve2Polylines

Keywords:

piecewise linear approximation polyline

SymbCrv3DCurvatureNormal

(symb_lib/curvatur.c:267)

Prototype:

  CagdCrvStruct *SymbCrv3DCurvatureNormal(CagdCrvStruct *Crv)


Description:

Computes a vector field curve representing the curvature of a curve, in the normal direction, that is kN. 
               .   ..      .       .   ..     .
               C x C       C     ( C x C  ) x C
kN = kB x T =  -----  x  ----- = --------------
                 .  3      .           .  4
               | C |     | C |       | C |


Parameters:



 Crv:        To compute the normal curvature field.




Returned Value:



  CagdCrvStruct *:   Computed normal curvature field.




See Also:

  SymbCrv2DCurvatureSqr
  SymbCrv3DCurvatureSqr
  SymbCrv3DCurvatureSqr
  
  SymbCrv3DRadiusNormal
  SymbCrv2DCurvatureSign
  SymbCrv2DInflectionPts
  
  SymbCrv2DExtremCrvtrPts


Keywords:

  curvature


 SymbCrv3DCurvatureSqr 
  (symb_lib/curvatur.c:134)

Prototype:

  CagdCrvStruct *SymbCrv3DCurvatureSqr(CagdCrvStruct *Crv)



Description:


Computes a scalar field curve representing the square of the curvature of a given 3D curve.

Parameters:

Crv: To compute scalar field of curvatrue square for.


Returned Value:

CagdCrvStruct *: Computed scalar field of curvature square of Crv.


See Also:

SymbCrv2DCurvatureSqr SymbCrv3DRadiusNormal SymbCrv3DCurvatureNormal SymbCrv2DCurvatureSign SymbCrv2DInflectionPts SymbCrv2DExtremCrvtrPts

Keywords:

curvature

SymbCrv3DRadiusNormal

(symb_lib/curvatur.c:203)

Prototype:

  CagdCrvStruct *SymbCrv3DRadiusNormal(CagdCrvStruct *Crv)


Description:

Computes a vector field curve representing the radius (1/curvature) of a curve, in the normal direction, that is N / k: 
                  .   ..    .      .  6        .   ..    .     .  2
         k N     (C x C ) x C    | C |      ( (C x C ) x C ) | C |
N / k =  ----- = ------------ . --------- = -----------------------
           2          .  4       .   .. 2           .   .. 2
          k         | C |       (C x C )           (C x C )


Parameters:



 Crv:        To compute the normal field with radius as magnitude.




Returned Value:



  CagdCrvStruct *:   Computed normal field with 1 / k as magnitude.




See Also:

  SymbCrv2DCurvatureSqr
  SymbCrv3DCurvatureSqr
  SymbCrv3DCurvatureSqr
  
  SymbCrv3DCurvatureNormal
  SymbCrv2DCurvatureSign
  
  SymbCrv2DInflectionPts
  SymbCrv2DExtremCrvtrPts


Keywords:

  curvature


 SymbCrvAdapOffset 
  (symb_lib/offset.c:461)

Prototype:

  CagdCrvStruct *SymbCrvAdapOffset(CagdCrvStruct *OrigCrv,
                                   CagdRType OffsetDist,
                                   CagdRType OffsetError,
                                   SymbOffCrvFuncType OffsetAprxFunc,
                                   CagdBType BezInterp)



Description:


Given a curve and an offset amount OffsetDist, returns an approximation to the offset curve by offseting the control polygon in the normal direction. This function computes an approximation to the offset using OffsetAprxFunc, measure the error and use it to refine and decrease the error adaptively. Bezier curves are promoted to Bsplines curves. See also: Gershon Elber and Elaine Cohen, "Error Bounded Variable Distance Offset Operator for Free Form Curves and Surfaces". International Journal of Computational Geometry & Applications, Vol. 1, Num. 1, March 1991, pp 67-78.

Parameters:

OrigCrv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
OffsetError: Tolerance control.
OffsetAprxFunc: A function that can be used to approximate an offset of a curve. If NULL SymbCrvOffset function is selected.
BezInterp: If TRUE, control points are interpolated when the curve is reduced to a Bezier form. Otherwise, control points are translated OffsetDist amount only, under estimating the Offset.


Returned Value:

CagdCrvStruct *: An approximation to the offset curve, to within OffsetError.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbCrvAdapOffsetTrim

(symb_lib/offset.c:592)

Prototype:

  CagdCrvStruct *SymbCrvAdapOffsetTrim(CagdCrvStruct *OrigCrv,
                                       CagdRType OffsetDist,
                                       CagdRType OffsetError,
                                       SymbOffCrvFuncType OffsetAprxFunc,
                                       CagdBType BezInterp)


Description:

Same function as CagdCrvAdapOffset, but trims the self intersection loops. See also: Gershon Elber and Elaine Cohen, "Error Bounded Variable Distance Offset Operator for Free Form Curves and Surfaces". International Journal of Computational Geometry & Applications, Vol. 1, Num. 1, March 1991, pp 67-78.

Parameters:

OrigCrv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
OffsetError: Tolerance control.
OffsetAprxFunc: A function that can be used to approximate an offset of a curve. If NULL SymbCrvOffset function is selected. Third parameter of SymbOffCrvFuncType is optional.
BezInterp: If TRUE, control points are interpolated when the curve is reduced to a Bezier form. Otherwise, control points are translated OffsetDist amount only, under estimating the Offset.


Returned Value:

CagdCrvStruct *: An approximation to the offset curve, to within OffsetError.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbCrvAdd

(symb_lib/symbolic.c:39)

Prototype:

  CagdCrvStruct *SymbCrvAdd(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - add them coordinatewise. The two curves are promoted to same point type before the multiplication can take place. Furthermore, order and continuity are matched as well.

Parameters:

Crv1, Crv2: Two curve to add up coordinatewise.


Returned Value:

CagdCrvStruct *: The summation of Crv1 + Crv2 coordinatewise.


See Also:

SymbCrvSub SymbCrvMult

Keywords:

addition symbolic computation

SymbCrvArcLen

(symb_lib/arc_len.c:387)

Prototype:

  CagdRType SymbCrvArcLen(CagdCrvStruct *Crv, CagdRType Epsilon)


Description:

Computes a tight approximation to the arc length of a curve. Estimates the arc length scalar field of Crv using SymbCrvArcLenCrv and evaluate the estimate on the curve's domain boundary.

Parameters:

Crv: Curve to compute a tight approximation on arc length.
Epsilon: Accuracy control.


Returned Value:

CagdRType: The approximated arc length of the given curve Crv.


Keywords:

arc length

SymbCrvArcLenCrv

(symb_lib/arc_len.c:356)

Prototype:

  CagdCrvStruct *SymbCrvArcLenCrv(CagdCrvStruct *Crv, CagdRType Epsilon)


Description:

Computes a scalar curve approximating the arc length of given curve Crv. Arc length is astimated by computing the square of Crv first derivative approximating its square root and integrating symbolically.

Parameters:

Crv: To approximate its arc length scalar field.
Epsilon: Accuracy of approximating.


Returned Value:

CagdCrvStruct *: A scalar field approximating Crv arc length.


Keywords:

arc length

SymbCrvArcLenPoly

(symb_lib/arc_len.c:71)

Prototype:

  CagdRType SymbCrvArcLenPoly(CagdCrvStruct *Crv)


Description:

Computes a bound on the arc length of a curve by computing the length of its control polygon.

Parameters:

Crv: To bound its length.


Returned Value:

CagdRType: An upper bound on the curve Crv length as the length of Crv's control polygon.


Keywords:

arc length

SymbCrvArcLenSteps

(symb_lib/arc_len.c:419)

Prototype:

  CagdPtStruct *SymbCrvArcLenSteps(CagdCrvStruct *Crv,
                                   CagdRType Length,
                                   CagdRType Epsilon)


Description:

Computes parameter values to move steps of Length at a time on curve Crv. Returned is a list of parameter values to move along.

Parameters:

Crv: Curve to compute constant arc Length steps.
Length: The step size.
Epsilon: Accuracy control.


Returned Value:

CagdPtStruct *: List of parameter values to march along Crv with arc Length between them.


Keywords:

arc length

SymbCrvConstSet

(symb_lib/symbzero.c:149)

Prototype:

  CagdPtStruct *SymbCrvConstSet(CagdCrvStruct *Crv,
                                int Axis,
                                CagdRType Epsilon,
                                CagdRType ConstVal)


Description:

Computes the constant set of a given curve, in the given axis (1-3 for X-Z). Returned is a list of the constant set points holding the parameter values at Pt[0] of each point.

Parameters:

Crv: To compute its constant set.
Axis: The axis of Crv to compute constant set for.
Epsilon: Tolerance control.
ConstVal: The value at which to compute the constant set.


Returned Value:

CagdPtStruct *: List of parameter values form which Crv has an value of ConstVal in axis Axis.


Keywords:

constant set zero set symbolic computation

SymbCrvCrossProd

(symb_lib/symbolic.c:380)

Prototype:

  CagdCrvStruct *SymbCrvCrossProd(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - computes their cross product. Returned curve is a scalar curve representing the cross product of the two given curves.

Parameters:

Crv1, Crv2: Two curve to multiply and compute a cross product for.


Returned Value:

CagdCrvStruct *: A scalar curve representing the cross product of Crv1 x Crv2.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvMult SymbCrvMultScalar

Keywords:

product cross product symbolic computation

SymbCrvCrvConvolution

(symb_lib/offset.c:913)

Prototype:

  CagdCrvStruct *SymbCrvCrvConvolution(CagdCrvStruct *Crv1,
                                       CagdCrvStruct *Crv2,
                                       CagdRType OffsetDist,
                                       CagdRType Tolerance)


Description:

Computes the convolution of the given two curves by matching their tangents and reparametrizing Crv2. If Crv2 is NULL, an Arc of radius OffsetDist is used, resulting in an offset operation of Crv1. Both Crv1 and Crv2 are assumed to have no inflection points and to span the same angular domain. That is Crv1'(0) || Crv2'(0) and similarly Crv1'(1) || Crv2'(1), where || denotes parallel.

Parameters:

Crv1, Crv2: The two curves to convolve.
OffsetDist: Amount of offset, if Crv2 == NULL. Negative value denotes other offset/convolution direction.
Tolerance: Of angular discrepancy that is allowed.


Returned Value:

CagdCrvStruct *: The offset curve approximation.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:



SymbCrvDotProd

(symb_lib/symbolic.c:203)

Prototype:

  CagdCrvStruct *SymbCrvDotProd(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - computes their dot product. Returned curve is a scalar curve representing the dot product of the two given curves.

Parameters:

Crv1, Crv2: Two curve to multiply and compute a dot product for.


Returned Value:

CagdCrvStruct *: A scalar curve representing the dot product of Crv1 . Crv2.


See Also:

SymbCrvScalarScale SymbCrvVecDotProd SymbCrvMult SymbCrvMultScalar

Keywords:

product dot product symbolic computation

SymbCrvEnclosedArea

(symb_lib/symbolic.c:656)

Prototype:

  CagdCrvStruct *SymbCrvEnclosedArea(CagdCrvStruct *Crv)


Description:

Given a planar curve, compute its enclosed area field curve. This has little meaning unless Crv is closed, in which by evaluation the resulting area filed curve at the end points, the area enclosed by Crv can be computed.

Parameters:

Crv: A curve to compute area filed curve for.


Returned Value:

CagdCrvStruct *: The area field curve.


Keywords:

area symbolic computation

SymbCrvExtremSet

(symb_lib/symbzero.c:69)

Prototype:

  CagdPtStruct *SymbCrvExtremSet(CagdCrvStruct *Crv, int Axis, CagdRType Epsilon)


Description:

Computes the extremum set of a given curve, in given axis (1-3 for X-Z). Returned is a list of the extreme set points holding the parameter values at Pt[0] of each point. One could compute the derivative of the curve and find its zero set. However, for rational curves, this will double the degree and slow down the computation considerably.

Parameters:

Crv: To compute its extremum set.
Axis: The axis of Crv to compute extremum set for.
Epsilon: Tolerance control.


Returned Value:

CagdPtStruct *: List of parameter values form which Crv has an extremum value in axis Axis.


Keywords:

extremum set symbolic computation

SymbCrvInvert

(symb_lib/symbolic.c:123)

Prototype:

  CagdCrvStruct *SymbCrvInvert(CagdCrvStruct *Crv)


Description:

Given a scalar curve, returns a scalar curve representing the reciprocal values, by making it rational (if was not one) and flipping the numerator and the denominator.

Parameters:

Crv: A scalar curve to compute a reciprocal value for.


Returned Value:

CagdCrvStruct *: A rational scalar curve that is equalto the reciprocal value of Crv.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvMult SymbCrvMultScalar

Keywords:

division symbolic computation reciprocal value

SymbCrvLeastSquarOffset

(symb_lib/offset.c:768)

Prototype:

  CagdCrvStruct *SymbCrvLeastSquarOffset(CagdCrvStruct *Crv,
                                         CagdRType OffsetDist,
                                         int NumOfSamples,
                                         int NumOfDOF,
                                         int Order,
                                         CagdRType *Tolerance)


Description:

Given a curve and an offset amount OffsetDist, returns an approximation to the offset curve by least square fitting a curve to samples taken on the offset curve. Resulting curve of order Order (degree of Crv if Order == 0) will have NumOfDOF control points that least sqaure fit NumOfSamples samples on the offset curve. Tolerance will be updated to hold an error distance measure.

Parameters:

Crv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
NumOfSamples: umber of samples to sample the offset curve at.
NumOfDOF: Number of degrees of freedom on the newly computed offset approximation. This is thesame as the number of control points the new curve will have.
Order: Of the newly constructed offset approximation. If equal to zero, the order of Crv will be used.
Tolerance: To return an error estimate in the L-infinity norm.


Returned Value:

CagdCrvStruct *: An approximation to the offset curve.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvMatchingOffset

Keywords:

offset

SymbCrvMatchingOffset

(symb_lib/offset.c:850)

Prototype:

  CagdCrvStruct *SymbCrvMatchingOffset(CagdCrvStruct *Crv,
                                       CagdRType OffsetDist,
                                       CagdRType Tolerance)


Description:

Computes an offset to a freeform curve using matching of tangent fields. The given curve is split at all its inflection points, made sure it spans less than 90 degrees, and then is matched against an arc of the proper angular span of tangents. Unlike other offset methods, this method allways preserves the distance between the original curve ans its offset. The error in this methods can surface only in the non orthogonality of the offset direction.

Parameters:

Crv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
Tolerance: Of angular discrepancy that is allowed.


Returned Value:

CagdCrvStruct *: The offset curve approximation.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvCrvConvolution

Keywords:



SymbCrvMergeScalar

(symb_lib/symbolic.c:1442)

Prototype:

  CagdCrvStruct *SymbCrvMergeScalar(CagdCrvStruct *CrvW,
                                    CagdCrvStruct *CrvX,
                                    CagdCrvStruct *CrvY,
                                    CagdCrvStruct *CrvZ)


Description:

Given a set of scalar curves, treat them as coordinates into a new curve. Assumes at least CrvX is not NULL in which a scalar curve is returned. Assumes CrvX/Y/Z/W are either E1 or P1 in which the weights are assumed to be identical and can be ignored if CrvW exists or copied otheriwse.

Parameters:

CrvW: The weight component of new constructed curve, if have any.
CrvX: The X component of new constructed curve.
CrvY: The Y component of new constructed curve, if have any.
CrvZ: The Z component of new constructed curve, if have any.


Returned Value:

CagdCrvStruct *: A new curve constructed from given scalar curves.


See Also:

SymbSrfMergeScalar SymbCrvSplitScalar

Keywords:

merge symbolic computation

SymbCrvMult

(symb_lib/symbolic.c:85)

Prototype:

  CagdCrvStruct *SymbCrvMult(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - multiply them coordinatewise. The two curves are promoted to same point type before the multiplication can take place.

Parameters:

Crv1, Crv2: Two curve to multiply coordinatewise.


Returned Value:

CagdCrvStruct *: The product of Crv1 * Crv2 coordinatewise.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvInvert SymbCrvMultScalar

Keywords:

product symbolic computation

SymbCrvMultScalar

(symb_lib/symbolic.c:312)

Prototype:

  CagdCrvStruct *SymbCrvMultScalar(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - a vector curve Crv1 and a scalar curve Crv2, multiply all Crv1's coordinates by the scalar curve Crv2. Returned curve is a curve representing the product of the two given curves.

Parameters:

Crv1, Crv2: Two curve to multiply.


Returned Value:

CagdCrvStruct *: A curve representing the product of Crv1 and Crv2.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvMult SymbCrvCrossProd

Keywords:

product symbolic computation

SymbCrvMultiResCompos

(symb_lib/multires.c:237)

Prototype:

  CagdCrvStruct *SymbCrvMultiResCompos(SymbMultiResCrvStruct *MRCrv)


Description:

Given a multi resolution decomposition of a Bspline curve, computes the regular Bspline curve out of it. *

Parameters:

MRCrv: A multi resolution decomposition of a curve.


Returned Value:

CagdCrvStruct *: A curve that adds up all components of the multi resolution decomposition MRCrv.


Keywords:

multi resolution least square decomposition

SymbCrvMultiResComposAtT

(symb_lib/multires.c:266)

Prototype:

  CagdCrvStruct *SymbCrvMultiResComposAtT(SymbMultiResCrvStruct *MRCrv,
                                          CagdRType T)


Description:

Given a multi resolution decomposition of a Bspline curve, computes a regular Bspline curve out of it representing the decomposed curve at the multi resolution hierarchy level of T. Although decomposition is discrete, T can be any real number between these discrete levels and a linear interpolation of adjacent levels is exploited.

Parameters:

MRCrv: A multi resolution decomposition of a curve.
T: A mult resolution hierarcy level to compute curve for.


Returned Value:

CagdCrvStruct *: A curve that adds up all components of the multi resolution decomposition MRCrv up to and including level T.


Keywords:

multi resolution least square decomposition

SymbCrvMultiResCopy

(symb_lib/multires.c:575)

Prototype:

  SymbMultiResCrvStruct *SymbCrvMultiResCopy(SymbMultiResCrvStruct *MRCrvOrig)


Description:

Given a multi resolution decomposition of a Bspline curve, copy it.

Parameters:

MRCrv: A multi resolution decomposition of a curve to copy.


Returned Value:

SymbMultiResCrvStruct *: A duplicated structure of MRCrv.


Keywords:

multi resolution least square decomposition

SymbCrvMultiResDecomp

(symb_lib/multires.c:37)

Prototype:

  SymbMultiResCrvStruct *SymbCrvMultiResDecomp(CagdCrvStruct *Crv, int Discont)


Description:

Given a Bspline curve, computes a hierarch of Bspline curves, each being represented using a subspace of the previous, upto a curve with no interior knots (i.e. a polynomial Bezier). However, if Discont == TRUE, then C1 discontinuities are preserved through out the hierarchy decomposition. Each level in hierarchy has approximately half the number of control points of the previous one. Least square curve fitting is used to build the hierarchy.

Parameters:

Crv: To compute a least square multi resolution decomposition for.
Discont: Do we want to preserve discontinuities?


Returned Value:

SymbMultiResCrvStruct *: A multi resolution curve structure hold the multi resolution decomposition of Crv.


Keywords:

multi resolution least square decomposition

SymbCrvMultiResEdit

(symb_lib/multires.c:325)

Prototype:

  void SymbCrvMultiResEdit(SymbMultiResCrvStruct *MRCrv,
                           CagdRType t,
                           CagdVType TransDir,
                           CagdRType Level,
                           CagdRType FracLevel)


Description:

Given a multi resolution decomposition of a Bspline curve, edit it by modifying its Level'th Level according to the TransDir of Position at parametr t. Level can be a fraction number between the discrete levels of the decomposition denoting a linear blend of two neighboring discrete levels. Editing is performed in place.

Parameters:

MRCrv: A multi resolution decomposition of a curve to edit it in place.
t: Parameter value at which to modify MRCrv.
TransDir: Directional tranlation transformation to apply.
Level: Of multi resolution hierarchy to edit.
FracLevel: The fraction level to edit - will blend two neighboring levels.
SpanDiscont: re we allowed to cross over discontinuities?


Returned Value:

void


Keywords:

multi resolution least square decomposition

SymbCrvMultiResFree

(symb_lib/multires.c:514)

Prototype:

  void SymbCrvMultiResFree(SymbMultiResCrvStruct *MRCrv)


Description:

Given a multi resolution decomposition of a Bspline curve, free it.

Parameters:

MRCrv: A multi resolution decomposition of a curve to free.


Returned Value:

void


Keywords:

multi resolution least square decomposition

SymbCrvMultiResNew

(symb_lib/multires.c:544)

Prototype:

  SymbMultiResCrvStruct *SymbCrvMultiResNew(int Levels, CagdBType Periodic)


Description:

Allocates a data structure for multi resolution decomposition of a Bspline curve of Levels levels and possiblt periodic.

Parameters:

Levels: Number of levels to expect in the decomposition.
Periodic: Is the curve periodic?


Returned Value:

SymbMultiResCrvStruct *: A structure to hold a multi resolution decomposition of a curve of Levels levels.


Keywords:

multi resolution least square decomposition

SymbCrvMultiResRefineLevel

(symb_lib/multires.c:432)

Prototype:

  CagdRType *SymbCrvMultiResRefineLevel(SymbMultiResCrvStruct *MRCrv,
                                        CagdRType T,
                                        int SpanDiscont)


Description:

Given a multi resolution decomposition of a Bspline curve, refine it at neighborhood of parameter value t, in place.

Parameters:

MRCrv: A multi resolution decomposition of a curve, to refine in place.
T: Parameter value at which to refine MRCrv.
SpanDiscont: o we want to refine beyond discontinuities?


Returned Value:

CagdRType *: A pointer to an array of two real numbers holding the domain in MRCrv that was refined.


Keywords:

multi resolution least square decomposition

SymbCrvOffset

(symb_lib/offset.c:51)

Prototype:

  CagdCrvStruct *SymbCrvOffset(CagdCrvStruct *Crv,
                               CagdRType OffsetDist,
                               CagdBType BezInterp)


Description:

Given a curve and an offset amount OffsetDist, returns an approximation to the offset curve by offseting the control polygon in the normal direction.

Parameters:

Crv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
BezInterp: If TRUE, control points are interpolated when the curve is reduced to a Bezier form. Otherwise, control points are translated OffsetDist amount only, under estimating the Offset.


Returned Value:

CagdCrvStruct *: An approximation to the offset curve.


See Also:

SymbCrvSubdivOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbCrvPosNegWeights

(symb_lib/symbzero.c:369)

Prototype:

  CagdBType SymbCrvPosNegWeights(CagdCrvStruct *Crv)


Description:

Returns TRUE iff the Crv is not rational or rational with weights that are entirely positive or entirely negative.

Parameters:

Crv: To examine for same sign weights, if any.


Returned Value:

CagdBType: TRUE if no weights or all of same sign.


Keywords:

symbolic computation

SymbCrvRtnlMult

(symb_lib/symbolic.c:498)

Prototype:

  CagdCrvStruct *SymbCrvRtnlMult(CagdCrvStruct *Crv1X,
                                 CagdCrvStruct *Crv1W,
                                 CagdCrvStruct *Crv2X,
                                 CagdCrvStruct *Crv2W,
                                 CagdBType OperationAdd)


Description:

Given two curves - multiply them using the quotient product rule: 
 X = X1 W2 +/- X2 W1

All provided curves are assumed to be non rational scalar curves. Returned is a non rational scalar curve (CAGD_PT_E1_TYPE).

Parameters:

Crv1X: Numerator of first curve.
Crv1W: Denominator of first curve.
Crv2X: Numerator of second curve.
Crv2W: Denominator of second curve.
OperationAdd: TRUE for addition, FALSE for subtraction.


Returned Value:

CagdCrvStruct *: The result of Crv1X Crv2W +/- Crv2X Crv1W.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvMult SymbCrvMultScalar

Keywords:

product symbolic computation

SymbCrvScalarScale

(symb_lib/symbolic.c:170)

Prototype:

  CagdCrvStruct *SymbCrvScalarScale(CagdCrvStruct *Crv, CagdRType Scale)


Description:

Given a curve, scale it by Scale.

Parameters:

Crv: A curve to scale by magnitude Scale.
Scale: Scaling factor.


Returned Value:

CagdCrvStruct *: A curves scaled by Scale compared to Crv.


See Also:

SymbCrvDotProd SymbCrvVecDotProd SymbCrvMult SymbCrvMultScalar

Keywords:

scaling symbolic computation

SymbCrvSplitScalar

(symb_lib/symbolic.c:1387)

Prototype:

  void SymbCrvSplitScalar(CagdCrvStruct *Crv,
                          CagdCrvStruct **CrvW,
                          CagdCrvStruct **CrvX,
                          CagdCrvStruct **CrvY,
                          CagdCrvStruct **CrvZ)


Description:

Given a curve splits it to its scalar component curves. Ignores all dimensions beyond the third, Z, dimension.

Parameters:

Crv: Curve to split.
CrvW: The weight component of Crv, if have any.
CrvX: The X component of Crv.
CrvY: The Y component of Crv, if have any.
CrvZ: The Z component of Crv, if have any.


Returned Value:

void


See Also:

SymbSrfSplitScalar SymbCrvMergeScalar

Keywords:

split symbolic computation

SymbCrvSqrtScalar

(symb_lib/arc_len.c:244)

Prototype:

  CagdCrvStruct *SymbCrvSqrtScalar(CagdCrvStruct *OrigCrv, CagdRType Epsilon)


Description:

Computes the curve which is a square root approximation to a given scalar curve, to within epsilon.

Parameters:

OrigCrv: Scalar curve to approximate its square root function.
Epsilon: Accuracy of approximation.


Returned Value:

CagdCrvStruct *: A curve approximating the square root of OrigCrv.


Keywords:

square root

SymbCrvSub

(symb_lib/symbolic.c:62)

Prototype:

  CagdCrvStruct *SymbCrvSub(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves - subtract them coordinatewise. The two curves are promoted to same point type before the multiplication can take place. Furthermore, order and continuity are matched as well.

Parameters:

Crv1, Crv2: Two curve to subtract coordinatewise.


Returned Value:

CagdCrvStruct *: The difference of Crv1 - Crv2 coordinatewise.


See Also:

SymbCrvAdd SymbCrvMult

Keywords:

subtraction symbolic computation

SymbCrvSubdivOffset

(symb_lib/offset.c:183)

Prototype:

  CagdCrvStruct *SymbCrvSubdivOffset(CagdCrvStruct *Crv,
                                     CagdRType OffsetDist,
                                     CagdRType Tolerance,
                                     CagdBType BezInterp)


Description:

Given a curve and an offset amount OffsetDist, returns an approximation to the offset curve by offseting the control polygon in the normal direction. If resulting offset is not satisfying the required tolerance the curve is subdivided and the algorithm recurses on both parts.

Parameters:

Crv: To approximate its offset curve with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
Tolerance: Accuracy control.
BezInterp: If TRUE, control points are interpolated when the curve is reduced to a Bezier form. Otherwise, control points are translated OffsetDist amount only, under estimating the Offset.


Returned Value:

CagdCrvStruct *: An approximation to the offset curve, to within Tolerance.


See Also:

SymbCrvOffset SymbSrfOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbCrvUnitLenScalar

(symb_lib/arc_len.c:112)

Prototype:

  CagdCrvStruct *SymbCrvUnitLenScalar(CagdCrvStruct *OrigCrv,
                                      CagdBType Mult,
                                      CagdRType Epsilon)


Description:

Normalizes the given vector field curve to be a unit length curve, by computing a scalar curve to multiply with this vector field curve. Returns the multiplied curve if Mult, or otherwise just the scalar curve.

Parameters:

OrigCrv: Curve to approximate a unit size for.
Mult: Do we want to multiply the computed scalar curve with Crv?
Epsilon: Accuracy required of this approximation.


Returned Value:

CagdCrvStruct *: A scalar curve to multiply OrigCrv so a unit size curve will return if Mult is FALSE, or the actual unit size vector field curve, if Mult.


Keywords:

unit vector field

SymbCrvVecDotProd

(symb_lib/symbolic.c:252)

Prototype:

  CagdCrvStruct *SymbCrvVecDotProd(CagdCrvStruct *Crv, CagdVType Vec)


Description:

Given a curve and a vector - computes their dot product. Returned curve is a scalar curve representing the dot product.

Parameters:

Crv: Curve to multiply and compute a dot product for.
Vec: Vector to project Crv onto.


Returned Value:

CagdCrvStruct *: A scalar curve representing the dot product of Crv . Vec.


See Also:

SymbCrvDotProd SymbCrvMult SymbCrvMultScalar SymbCrvCrossProd

Keywords:

product dot product symbolic computation

SymbCrvZeroSet

(symb_lib/symbzero.c:43)

Prototype:

  CagdPtStruct *SymbCrvZeroSet(CagdCrvStruct *Crv, int Axis, CagdRType Epsilon)


Description:

Computes the zero set of a given curve, in the given axis (1-3 for X-Z). Returned is a list of the zero set points holding the parameter values att Pt[0] of each point.

Parameters:

Crv: To compute its zero set.
Axis: The axis of Crv to compute zero set for.
Epsilon: Tolerance control.


Returned Value:

CagdPtStruct *: List of parameter values form which Crv is zero in axis Axis.


Keywords:

zero set symbolic computation

SymbDescribeError

(symb_lib/symb_err.c:67)

Prototype:

  char *SymbDescribeError(SymbFatalErrorType ErrorNum)


Description:

Returns a string describing a the given error. Errors can be raised by any member of this symb library as well as other users. Raised error will cause an invokation of SymbFatalError function which decides how to handle this error. SymbFatalError can for example, invoke this routine with the error type, print the appropriate message and quit the program.

Parameters:

ErrorNum: Type of the error that was raised.


Returned Value:

char *: A string describing the error type.


Keywords:

error handling

SymbDistCrvLine

(symb_lib/distance.c:166)

Prototype:

  CagdRType SymbDistCrvLine(CagdCrvStruct *Crv,
                            CagdLType Line,
                            CagdBType MinDist,
                            CagdRType Epsilon)


Description:

Given a curve and a line, finds the nearest point (if MinDist) or the farest location (if MinDist FALSE) from the curve to the given line. Returned is the parameter value of the curve. Let Crv be (x(t), y(t)). By substituting x(t) and y(t) into the line equation, we derive the distance function. Its zero set, combined with the zero set of its derivative provide the needed extreme distances.

Parameters:

Crv: The curve to find its nearest (farest) point to Line.
Line: The line to find the nearest (farest) point on Crv to it.
MinDist: If TRUE nearest points is needed, if FALSE farest.
Epsilon: Accuracy of computation.


Returned Value:

CagdRType: Parameter value in the parameter space of Crv of the nearest (farest) point to line Line.


Keywords:

curve line distance

SymbDistCrvPoint

(symb_lib/distance.c:47)

Prototype:

  CagdRType SymbDistCrvPoint(CagdCrvStruct *Crv,
                             CagdPType Pt,
                             CagdBType MinDist,
                             CagdRType Epsilon)


Description:

Given a curve and a point, finds the nearest point (if MinDist) or the farest location (if MinDist FALSE) from the curve to the given point. Returned is the parameter value of the curve. Computes the zero set of (Crv(t) - Pt) . Crv'(t).

Parameters:

Crv: The curve to find its nearest (farest) point to Pt.
Pt: The point to find the nearest (farest) point on Crv to it.
MinDist: If TRUE nearest points is needed, if FALSE farest.
Epsilon: Accuracy of computation.


Returned Value:

CagdRType: Parameter value in the parameter space of Crv of the nearest (farest) point to point Pt.


Keywords:

curve point distance

SymbExtremumCntPtVals

(symb_lib/symbolic.c:1742)

Prototype:

  CagdRType *SymbExtremumCntPtVals(CagdRType **Points,
                                   int Length,
                                   CagdBType FindMinimum)


Description:

Given a control polygon/mesh, computes the extremum values of them all.

Parameters:

Points: To scan for extremum values.
Length: Length of each vector in Points.
FindMinimum: TRUE for minimum, FALSE for maximum.


Returned Value:

CagdRType *: A vector holding PType point with the extremum values of each axis independently.


Keywords:

extremum values symbolic computation

SymbFatalError

(symb_lib/symb_ftl.c:27)

Prototype:

  void SymbFatalError(SymbFatalErrorType ErrID)


Description:

Trap Symb_lib errors right here. Provides a default error handler for the symb library. Gets an error description using SymbDescribeError, prints it and exit the program using exit.

Parameters:

ErrID: Error type that was raised.


Returned Value:

void


Keywords:

error handling

SymbLclDistCrvLine

(symb_lib/distance.c:241)

Prototype:

  CagdPtStruct *SymbLclDistCrvLine(CagdCrvStruct *Crv,
                                   CagdLType Line,
                                   CagdRType Epsilon,
                                   CagdBType InterPos,
                                   CagdBType ExtremPos)


Description:

Given a curve and a line, finds the local extreme distance points on the curve to the given line. Returned is a list of parameter value with local extreme distances. Let Crv be (x(t), y(t)). By substituting x(t) and y(t) into the line equation, we derive the distance function. Its zero set, possibly combined with the zero set of its derivative provide the needed extreme distances.

Parameters:

Crv: The curve to find its nearest (farest) point to Line.
Line: The line to find the nearest (farest) point on Crv to it.
Epsilon: Accuracy of computation.
InterPos: Do we want the intersection locations?
ExtremPos: Do we want the extremum distance locations?


Returned Value:

CagdPtStruct *: A list of parameter values of extreme distance locations.


Keywords:

curve line distance

SymbLclDistCrvPoint

(symb_lib/distance.c:116)

Prototype:

  CagdPtStruct *SymbLclDistCrvPoint(CagdCrvStruct *Crv,
                                    CagdPType Pt,
                                    CagdRType Epsilon)


Description:

Given a curve and a point, find the local extremum distance points on the curve to the given point. Returned is a list of parameter value with local extremum. Computes the zero set of (Crv(t) - Pt) . Crv'(t).

Parameters:

Crv: The curve to find its extreme distance locations to Pt.
Pt: The point to find the extreme distance locations from Crv.
Epsilon: Accuracy of computation.


Returned Value:

CagdPtStruct *: A list of parameter values of extreme distance locations.


Keywords:

curve point distance

SymbLimitCrvArcLen

(symb_lib/arc_len.c:31)

Prototype:

  CagdCrvStruct *SymbLimitCrvArcLen(CagdCrvStruct *Crv, CagdRType MaxLen)


Description:

Subdivides the given curves to curves, each with size of control polygon less than or equal to MaxLen. Returned is a list of curves.

Parameters:

Crv: To subdivide into curves, each with control polygon length less than MaxLen.
MaxLen: Maximum length of control polygon to allow.


Returned Value:

CagdCrvStruct *: List of subdivided curves from Crv, each with control polygon size of less than MaxLen.


Keywords:

arc length

SymbMakePosCrvCtlPolyPos

(symb_lib/curvatur.c:414)

Prototype:

  CagdCrvStruct *SymbMakePosCrvCtlPolyPos(CagdCrvStruct *OrigCrv)


Description:

Given a scalar curve that is positive, refine it until all its control points has positive coefficients. Always returns a Bspline curve.

Parameters:

OrigCrv: To refine until all its control points are non negative.


Returned Value:

CagdCrvStruct *: Refined positive curve with positive control points.


Keywords:

refinement

SymbMeshAddSub

(symb_lib/symbolic.c:1330)

Prototype:

  void SymbMeshAddSub(CagdRType **DestPoints,
                      CagdRType **Points1,
                      CagdRType **Points2,
                      CagdPointType PType,
                      int Size,
                      CagdBType OperationAdd)


Description:

Given two control polygons/meshes - add them coordinatewise. If mesh is rational, weights are assumed identical and are just copied.

Parameters:

DestPoints: Where addition or difference result should go to.
Points1: First control polygon/mesh.
Points2: Second control polygon/mesh.
PType: Type of points we are dealing with.
Size: Length of each vector in Points1/2.
OperationAdd: TRUE of addition, FALSE for subtraction.


Returned Value:

void


See Also:

SymbSrfSub SymbSrfAdd

Keywords:

addition subtraction symbolic computation

SymbNormalConeForSrf

(symb_lib/nrmlcone.c:31)

Prototype:

  SymbNormalConeStruct *SymbNormalConeForSrf(CagdSrfStruct *Srf)


Description:

Computes a normal cone for a given surface, by computing the normal field of the surface and deriving the angular span of this normal field by testing the angular span of all control vector in the normal field. A normal field is searched for as "_NormalSrf" attribute in Srf or computed locally of no such attribute is found.

Parameters:

Srf: To compute a normal cone for.


Returned Value:

SymbNormalConeStruct *: The computed normal cone.


See Also:

SymbNormalConeOverlap

Keywords:

normals normal bound

SymbNormalConeOverlap

(symb_lib/nrmlcone.c:123)

Prototype:

  CagdBType SymbNormalConeOverlap(SymbNormalConeStruct *NormalCone1,
                                  SymbNormalConeStruct *NormalCone2)


Description:

Tests if the given two normal cones overlap or not.

Parameters:

NormalCone1, NormalCone2: The two normal cones to test for angular overlap.


Returned Value:

CagdBType: TRUE if overlap, FALSE otherwise.


See Also:

SymbNormalConeOverlap

Keywords:

normals normal bound

SymbPiecewiseRuledSrfApprox

(symb_lib/prisa.c:122)

Prototype:

  CagdSrfStruct *SymbPiecewiseRuledSrfApprox(CagdSrfStruct *Srf,
                                             CagdBType ConsistentDir,
                                             CagdRType Epsilon,
                                             CagdSrfDirType Dir)


Description:

Constructs a piecewise ruled surface approximation to the given surface, Srf, in the given direction, Dir, that is close to the surface to within Epsilon. If ConsitentDir then ruled surface parametrization is set to be the same as original surface Srf. Otherwise, ruling dir is always CAGD_CONST_V_DIR. Surface is assumed to have point types E3 or P3 only.

Parameters:

Srf: To approximate using piecewise ruled surfaces.
ConsistentDir: o we want parametrization to be the same as Srf?
Epsilon: Accuracy of piecewise ruled surface approximation.
Dir: Direction of piecewise ruled surface approximation. Either U or V.


Returned Value:

CagdSrfStruct *: A list of ruled surfaces approximating Srf to within Epsilon in direction Dir.


Keywords:

layout prisa ruled surface approximation

SymbPrisaRuledSrf

(symb_lib/prisa.c:362)

Prototype:

  CagdSrfStruct *SymbPrisaRuledSrf(CagdSrfStruct *Srf,
                                   int SamplesPerCurve,
                                   CagdRType Space,
                                   CagdVType Offset)


Description:

Layout a single ruled surface, by approximating it as a set of polygons. The given ruled surface might be non-developable, in which case approximation will be of a surface with no twist. The ruled surface is assumed to be constructed using CagdRuledSrf and that the ruled direction is consisnt and is always CAGD_CONST_V_DIR.

Parameters:

Srf: A ruled surface to layout flat on the XY plane.
SamplesPerCurve: uring the approximation of a ruled surface as a developable surface.
Space: Increment on Y on the offset vector, after this surface was placed in the XY plane.
Offset: A vector in the XY plane to denote the amount of translation for the flatten surface in the XY plane.


Returned Value:

CagdSrfStruct *: A planar surface in the XY plane approximating the falttening process of Srf.


Keywords:

layout prisa

SymbPrmtSclrCrvTo2D

(symb_lib/symbolic.c:1640)

Prototype:

  CagdCrvStruct *SymbPrmtSclrCrvTo2D(CagdCrvStruct *Crv,
                                     CagdRType Min,
                                     CagdRType Max)


Description:

Promote a scalar curve to two dimensions by moving the scalar axis to be the Y axis and adding monotone X axis.

Parameters:

Crv: Scalar curve to promose to a two dimensional one.
Min: Minimum of new monotone X axis.
Max: Maximum of new monotone X axis.


Returned Value:

CagdCrvStruct *: A two dimensional curve.


See Also:

SymbPrmtSclrSrfTo3D

Keywords:

promotion conversion symbolic computation

SymbPrmtSclrSrfTo3D

(symb_lib/symbolic.c:1689)

Prototype:

  CagdSrfStruct *SymbPrmtSclrSrfTo3D(CagdSrfStruct *Srf,
                                     CagdRType UMin,
                                     CagdRType UMax,
                                     CagdRType VMin,
                                     CagdRType VMax)


Description:

Promote a scalar surface to three dimensions by moving the scalar axis to be the Z axis and adding monotone X and Y axes.

Parameters:

Srf:
UMin: Minimum of new monotone X axis.
UMax: Maximum of new monotone X axis.
VMin: Minimum of new monotone Y axis.
VMax: Maximum of new monotone X axis.


Returned Value:

CagdSrfStruct *: A three dimensional surface.


See Also:

SymbPrmtSclrCrvTo2D

Keywords:

promotion conversion symbolic computation

SymbSetAdapIsoExtractMinLevel

(symb_lib/adap_iso.c:57)

Prototype:

  void SymbSetAdapIsoExtractMinLevel(int MinLevel)


Description:

Sets minimum level of subdivision forced in the adaptive iso extraction.

Parameters:

MinLevel: At least that many subdivision will occur.


Returned Value:

void


Keywords:

adaptive isocurves

SymbSrf2Curves

(symb_lib/symbpoly.c:165)

Prototype:

  CagdCrvStruct *SymbSrf2Curves(CagdSrfStruct *Srf, int NumOfIsocurves[2])


Description:

Routine to extract from a surface NumOfIsoline isocurve list in each param. direction. Iso parametric curves are sampled equally spaced in parametric space. NULL is returned in case of an error, otherwise list of CagdCrvStruct.

Parameters:

Srf: To extract isoparametric curves from.
NumOfIsocurves: In each (U or V) direction.


Returned Value:

CagdCrvStruct *: List of extracted isoparametric curves. These curves inherit the order and continuity of the original Srf. NULL is returned in case of an error.


See Also:

BspSrf2PCurves BzrSrf2Curves

Keywords:

curves isoparametric curves

SymbSrf2DDeterminant

(symb_lib/curvatur.c:655)

Prototype:

  CagdSrfStruct *SymbSrf2DDeterminant(CagdSrfStruct *Srf11,
                                      CagdSrfStruct *Srf12,
                                      CagdSrfStruct *Srf21,
                                      CagdSrfStruct *Srf22)


Description:

Computes the expression of Srf11 * Srf22 - Srf12 * Srf21, which is a determinant of a 2 by 2 matrix.

Parameters:

Srf11, Srf12, Srf21, Srf22: The four factors of the determinant.


Returned Value:

CagdSrfStruct *: A scalar field representing the determinant computation.


See Also:

SymbSrfFff SymbSrfSff SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

determinant

SymbSrf2OptPolysBilinPolyError

(symb_lib/symbsply.c:290)

Prototype:

  CagdRType SymbSrf2OptPolysBilinPolyError(CagdSrfStruct *Srf,
                                           CagdSrfDirType Dir)


Description:

Routine to estimate the curvature of the patch using a bilinear approx.

Parameters:

Srf: To estimate curvature for.
Dir: Currently not used.


Returned Value:

CagdRType: Curvature estimated.


Keywords:

polygonization surface approximation

SymbSrf2OptPolysCurvatureError

(symb_lib/symbsply.c:201)

Prototype:

  CagdRType SymbSrf2OptPolysCurvatureError(CagdSrfStruct *Srf,
                                           CagdSrfDirType Dir)


Description:

Routine to estimate the curvature of the patch using k1^2 + k2^2. Assumes the availability of the GlblCrvtrSqrSrf for Srf. This estimate is too loose and in fact is not recommended!

Parameters:

Srf: To estimate curvature for.
Dir: Currently not used.


Returned Value:

CagdRType: Curvature estimated.


Keywords:

polygonization surface approximation

SymbSrf2OptPolysCurvatureErrorPrep

(symb_lib/symbsply.c:174)

Prototype:

  void SymbSrf2OptPolysCurvatureErrorPrep(CagdSrfStruct *Srf)


Description:

Routine to compute the scalar field of k1^2 + k2^2 (k1, k2 are principal curvatures) for the surface Srf, into GlblCrvtrSqrSrf. This scalar field is used by SymbSrf2OptPolysCurvatureError function.

Parameters:

Srf: To compute the curvature bound for as an optional preprocess for function SymbSrf2OptPolysCurvatureError.


Returned Value:

void


Keywords:

polygonization surface approximation

SymbSrf2OptPolysIsoDirCurvatureErrorPrep

(symb_lib/symbsply.c:357)

Prototype:

  void SymbSrf2OptPolysIsoDirCurvatureErrorPrep(CagdSrfStruct *Srf)


Description:

Routine to precompute the scalar field of kn^u and kn^v (the normal curvatures in the iso parametric directions). These scalar fields are used to determined the prefered subdivision location of Srf.

Parameters:

Srf: To compute the curvature bound in the isoparametric direction.


Returned Value:

void


Keywords:

polygonization surface approximation

SymbSrf2OptimalPolygons

(symb_lib/symbsply.c:402)

Prototype:

  CagdPolygonStruct *SymbSrf2OptimalPolygons(CagdSrfStruct *Srf,
                                  CagdRType Tolerance,
                                  SymbPlSubdivStrategyType SubdivDirStrategy,
                                  SymbPlErrorFuncType SrfPolyApproxErr,
                                  CagdBType ComputeNormals,
                                  CagdBType FourPerFlat,
                                  CagdBType ComputeUV)


Description:

Routine to convert a single surface to a set of triangles approximating it. FineNess is controlled via a function that returns an error measure SrfPolyApproxError that is guaranteed to be less than Tolerance.

Parameters:

Srf: To convert and approximate using triangles.
Tolerance: Accuracy control.
SubdivDirStrategy: lternatively in U and V, direction that minimizes the error, etc.
SrfPolyApproxErr: Using bilinear curvature estimate, k1^2 + k2^2 estimate, etc.
ComputeNormals: Do we want normals to be computed as well?
FourPerFlat: If TRUE, four triangle per flat surface patch are created, otherwise only two.
ComputeUV: Do we want UV parameter values with the vertices of the triangles?


Returned Value:

CagdPolygonStruct *: Resulting polygons that approximates Srf.


Keywords:

approximation conversion

SymbSrf2Polygons

(symb_lib/symbpoly.c:55)

Prototype:

  CagdPolygonStruct *SymbSrf2Polygons(CagdSrfStruct *Srf,
                                      int FineNess,
                                      CagdBType ComputeNormals,
                                      CagdBType FourPerFlat,
                                      CagdBType ComputeUV)


Description:

Routine to convert a single surface to set of triangles approximating it. FineNess is a fineness control on result and the larger it is more triangles may result. A value of 10 is a good starting value. NULL is returned in case of an error, otherwise list of CagdPolygonStruct.

Parameters:

Srf: To approximate into triangles.
FineNess: Control on accuracy, the higher the finer.
ComputeNormals: If TRUE, normal information is also computed.
FourPerFlat: If TRUE, four triangles are created per flat surface. If FALSE, only 2 triangles are created.
ComputeUV: If TRUE, UV values are stored and returned as well.


Returned Value:

CagdPolygonStruct *: A list of polygons with optional normal and/or UV parametric information. NULL is returned in case of an error.


See Also:

BzrSrf2Polygons IritSurface2Polygons IritTrimSrf2Polygons BspSrf2Polygons TrimSrf2Polygons

Keywords:

polygonization surface approximation

SymbSrf2Polylines

(symb_lib/symbpoly.c:110)

Prototype:

  CagdPolylineStruct *SymbSrf2Polylines(CagdSrfStruct *Srf,
                                        int NumOfIsocurves[2],
                                        int SamplesPerCurve,
                                        int Optimal)


Description:

Routine to convert a single surface to NumOfIsolines polylines in each parametric direction with SamplesPerCurve in each isoparametric curve. Polyline are always E3 of CagdPolylineStruct type. NULL is returned in case of an error, otherwise list of CagdPolylineStruct. Attempt is made to extract isolines along C1 discontinuities first.

Parameters:

Srf: Srf to extract isoparametric curves from.
NumOfIsocurves: To extarct from Srf in each (U or V) direction.
SamplesPerCurve: Fineness control on piecewise linear curve approximation.
Optimal: Use optimal approximation of isocurves.


Returned Value:

CagdPolylineStruct *: List of polylines representing a piecewise linear approximation of the extracted isoparamteric curves or NULL is case of an error.


See Also:

BspSrf2Polylines BzrSrf2Polylines IritSurface2Polylines IritTrimSrf2Polylines TrimSrf2Polylines

Keywords:

polylines isoparametric curves

SymbSrfAdd

(symb_lib/symbolic.c:732)

Prototype:

  CagdSrfStruct *SymbSrfAdd(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two surfaces - add them coordinatewise. The two surfaces are promoted to same point type before the multiplication can take place. Furthermore, order and continuity are matched as well.

Parameters:

Srf1, Srf2: Two surface to add up coordinatewise.


Returned Value:

CagdSrfStruct *: The summation of Srf1 + Srf2 coordinatewise.


See Also:

SymbSrfSub SymbMeshAddSub SymbSrfMult

Keywords:

addition symbolic computation

SymbSrfCrossProd

(symb_lib/symbolic.c:1021)

Prototype:

  CagdSrfStruct *SymbSrfCrossProd(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two surfaces - computes their cross product. Returned surface is a scalar surface representing the cross product of the two given surfaces.

Parameters:

Srf1, Srf2: Two surface to multiply and compute a cross product for.


Returned Value:

CagdSrfStruct *: A scalar surface representing the cross product of Srf1 x Srf2.


See Also:

SymbSrfDotProd SymbSrfVecDotProd SymbSrfScalarScale SymbSrfMultScalar SymbSrfInvert

Keywords:

product cross product symbolic computation

SymbSrfCurvatureUpperBound

(symb_lib/curvatur.c:1058)

Prototype:

  CagdSrfStruct *SymbSrfCurvatureUpperBound(CagdSrfStruct *Srf)


Description:

Computes curvature upper bound as Xi = k1^2 + k2^2, where k1 and k2 are the principal curvatures. Gij are the coefficients of the first fundamental form and Lij are of the second, using non unit normal n, 
     ( G11 L22 + G22 L11 - 2 G12 L12 )^2 - 2 |G| |L|
Xi = -----------------------------------------------
                           |G|^2 ||n||^2

See: "Second Order Surface Analysis Using Hybrid of Symbolic and Numeric Operators", By Gershon Elber and Elaine Cohen, Transaction on graphics, Vol. 12, No. 2, pp 160-178, April 1993.

Parameters:

Srf: Surface to compute curvature bound for.


Returned Value:

CagdSrfStruct *: A scalar field representing the curvature bound.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfIsoDirNormalCurvatureBound

Keywords:

curvature

SymbSrfDistCrvCrv

(symb_lib/distance.c:317)

Prototype:

  CagdSrfStruct *SymbSrfDistCrvCrv(CagdCrvStruct *Crv1, CagdCrvStruct *Crv2)


Description:

Given two curves, creates a bivariate scalar surface representing the distance function square, between them.

Parameters:

Crv1, Crv2: The two curves, Crv1(u) and Crv2(v), to form their distance function square between them as a bivariate function.


Returned Value:

CagdSrfStruct *: The distance function square d2(u, v) of the distance from Crv1(u) to Crv2(v).


See Also:

SymvCrvCrvInter SymbSrfDistFindPoints

Keywords:

curve curve distance

SymbSrfDistFindPoints

(symb_lib/distance.c:385)

Prototype:

  CagdPtStruct *SymbSrfDistFindPoints(CagdSrfStruct *Srf,
                                      CagdRType Epsilon,
                                      CagdBType SelfInter)


Description:

Given a scalar surface representing the distance function square between two curves, finds the zero set of the distance surface, if any, and returns it. The given surface is a non negative surface and zero set is its minima. The returned points will contain the two parameter values of the two curves that intersect in the detected zero set points.

Parameters:

Srf: A bivariate function that represent the distance square function between two curves.
Epsilon: Accuracy control.
SelfInter: Should we consider self intersection? That is, is Srf computed from a curve to itself!?


Returned Value:

CagdPtStruct *: A list of parameter values of both curves, at all detected intersection locations.


See Also:

SymbSrfDistCrvCrv SymvCrvCrvInter

Keywords:

curve curve distance curve curve intersection

SymbSrfDotProd

(symb_lib/symbolic.c:910)

Prototype:

  CagdSrfStruct *SymbSrfDotProd(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two surfaces - computes their dot product. Returned surface is a scalar surface representing the dot product of the two given surfaces.

Parameters:

Srf1, Srf2: Two surface to multiply and compute a dot product for.


Returned Value:

CagdSrfStruct *: A scalar surface representing the dot product of Srf1 . Srf2.


See Also:

SymbSrfMult SymbSrfVecDotProd SymbSrfScalarScale SymbSrfMultScalar SymbSrfInvert SymbSrfCrossProd

Keywords:

product dot product symbolic computation

SymbSrfFff

(symb_lib/curvatur.c:577)

Prototype:

  void SymbSrfFff(CagdSrfStruct *Srf,
                  CagdSrfStruct **DuSrf,
                  CagdSrfStruct **DvSrf,
                  CagdSrfStruct **FffG11,
                  CagdSrfStruct **FffG12,
                  CagdSrfStruct **FffG22)


Description:

Computes coefficients of the first fundamental form of given surface Srf.

Parameters:

Srf: Do compute the coefficients of the FFF for.
DuSrf: First derivative of Srf with respect to U goes to here.
DvSrf: First derivative of Srf with respect to V goes to here.
FffG11: FFF G11 scalar field.
FffG12: FFF G12 scalar field.
FffG22: FFF G22 scalar field.


Returned Value:

void


See Also:

SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

first fundamental form

SymbSrfFff

(symb_lib/curvatur.c:616)

Prototype:

  void SymbSrfSff(CagdSrfStruct *DuSrf,
                  CagdSrfStruct *DvSrf,
                  CagdSrfStruct **SffL11,
                  CagdSrfStruct **SffL12,
                  CagdSrfStruct **SffL22,
                  CagdSrfStruct **SNormal)


Description:

Computes coefficients of the first fundamental form of given surface Srf. These coefficients are using non normalized normal that is also returned.

Parameters:

DuSrf: First derivative of Srf with respect to U.
DvSrf: First derivative of Srf with respect to V.
SffL11: SFF L11 scalar field returned herein.
SffL12: SFF L12 scalar field returned herein.
SffL22: SFF L22 scalar field returned herein.
SNormal: Unnormalized normal vector field returned herein.


Returned Value:

void


See Also:

SymbSrfFff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

second fundamental form

SymbSrfGaussCurvature

(symb_lib/curvatur.c:685)

Prototype:

  CagdSrfStruct *SymbSrfGaussCurvature(CagdSrfStruct *Srf)


Description:

Computes the Gauss curvature of a given surface.

Parameters:

Srf: Surface to compute Gaussian curvature for.


Returned Value:

CagdSrfStruct *: A surface representing the Gaussian curvature field.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

curvature

SymbSrfInvert

(symb_lib/symbolic.c:819)

Prototype:

  CagdSrfStruct *SymbSrfInvert(CagdSrfStruct *Srf)


Description:

Given a scalar surface, returns a scalar surface representing the reciprocal values, by making it rational (if was not one) and flipping the numerator and the denominator.

Parameters:

Srf: A scalar surface to compute a reciprocal value for.


Returned Value:

CagdSrfStruct *: A rational scalar surface that is equalto the reciprocal value of Srf.


See Also:

SymbSrfDotProd SymbSrfVecDotProd SymbSrfScalarScale SymbSrfMultScalar SymbSrfMult SymbSrfCrossProd

Keywords:

division symbolic computation reciprocal value

SymbSrfIsoDirNormalCurvatureBound

(symb_lib/curvatur.c:1141)

Prototype:

  CagdSrfStruct *SymbSrfIsoDirNormalCurvatureBound(CagdSrfStruct *Srf,
                                                   CagdSrfDirType Dir)


Description:

Computes normal curvature bound in given isoparametric direction. This turns out to be (L11 . n) / G11 for u and (L22 . n) / G22 for v. Herein the square of these equations is computed symbolically and returned.

Parameters:

Srf: To compute normal curvature in an isoparametric direction Dir.
Dir: Direction to compute normal curvature. Either U or V.


Returned Value:

CagdSrfStruct *: A scalar field representing the normal curvature square of Srf in dirction Dir.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound

Keywords:

curvature

SymbSrfIsoFocalSrf

(symb_lib/curvatur.c:926)

Prototype:

  CagdSrfStruct *SymbSrfIsoFocalSrf(CagdSrfStruct *Srf, CagdSrfDirType Dir)


Description:

Computes a focal surface for a principal curvature in an isoparametric direction. For the u isoparametric direction, 
                      1               G11
F(u, v) = n(u, v) --------- = n(u, v) ---
                    u
                   k (u, v)           L11
                    n

Because Lii also has n(u,v) we can use the nonnormalized surface normal to compute F(u, v), which is therefore computable and representable.

Parameters:

Srf: Surface to compute iso focal surface.
Dir: Direction to compute iso focal surface. Either U or V.


Returned Value:

CagdSrfStruct *: A surface representing the iso focal surface.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfMeanCurvatureSqr SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

curvature focal surface evolute

SymbSrfMeanCurvatureSqr

(symb_lib/curvatur.c:882)

Prototype:

  CagdSrfStruct *SymbSrfMeanCurvatureSqr(CagdSrfStruct *Srf)


Description:

Computes the Mean curvature square of a given surface.

Parameters:

Srf: Surface to compute Mean curvature square for.


Returned Value:

CagdSrfStruct *: A surface representing the Mean curvature square field.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanEvolute SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

curvature

SymbSrfMeanEvolute

(symb_lib/curvatur.c:770)

Prototype:

  CagdSrfStruct *SymbSrfMeanEvolute(CagdSrfStruct *Srf)


Description:

Computes an "evolute surface" to a given surface using twice the Mean curvature as magnitude. 
                      1                             |G|
E(u, v) = n(u, v) --------- = n(u, v) ---------------------------------
                  2 H(u, v)           ( G11 L22 + G22 L11 - 2 G12 L12 )

Becuase H(u,v) also has n(u,v) we can use the nonnormalized surface normal to compute E(u, v), which is therefore computable and representable.

Parameters:

Srf: Surface to compute mean evolute.


Returned Value:

CagdSrfStruct *: A surface representing the mean evolute surface.


See Also:

SymbSrfFff SymbSrfSff SymbSrf2DDeterminant SymbSrfGaussCurvature SymbSrfMeanCurvatureSqr SymbSrfIsoFocalSrf SymbSrfCurvatureUpperBound SymbSrfIsoDirNormalCurvatureBound

Keywords:

curvature evolute

SymbSrfMergeScalar

(symb_lib/symbolic.c:1571)

Prototype:

  CagdSrfStruct *SymbSrfMergeScalar(CagdSrfStruct *SrfW,
                                    CagdSrfStruct *SrfX,
                                    CagdSrfStruct *SrfY,
                                    CagdSrfStruct *SrfZ)


Description:

Given a set of scalar surfaces, treat them as coordinates into a new surface. Assumes at least SrfX is not NULL in which a scalar surface is returned. Assumes SrfX/Y/Z/W are either E1 or P1 in which the weights are assumed to be identical and can be ignored if SrfW exists or copied otheriwse.

Parameters:

SrfW: The weight component of new constructed surface, if have any.
SrfX: The X component of new constructed surface.
SrfY: The Y component of new constructed surface, if have any.
SrfZ: The Z component of new constructed surface, if have any.


Returned Value:

CagdSrfStruct *: A new surface constructed from given scalar surfaces.


See Also:

SymbSrfSplitScalar SymbCrvMergeScalar

Keywords:

merge symbolic computation

SymbSrfMult

(symb_lib/symbolic.c:780)

Prototype:

  CagdSrfStruct *SymbSrfMult(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two surfaces - multiply them coordinatewise. The two surfaces are promoted to same point type before the multiplication can take place.

Parameters:

Srf1, Srf2: Two surface to multiply coordinatewise.


Returned Value:

CagdSrfStruct *: The product of Srf1 * Srf2 coordinatewise.


See Also:

SymbSrfDotProd SymbSrfVecDotProd SymbSrfScalarScale SymbSrfMultScalar SymbSrfInvert

Keywords:

product symbolic computation

SymbSrfNormalSrf

(symb_lib/symbolic.c:1173)

Prototype:

  CagdSrfStruct *SymbSrfNormalSrf(CagdSrfStruct *Srf)


Description:

Given a surface - compute its unnormalized norrmal vectorfield surface, as the cross product if this partial derivatives.

Parameters:

Srf: To compute an unnormalized normal vector field for.


Returned Value:

CagdSrfStruct *: A vector field representing the unnormalized normal vector field of Srf.


Keywords:

normal symbolic computation

SymbSrfOffset

(symb_lib/offset.c:259)

Prototype:

  CagdSrfStruct *SymbSrfOffset(CagdSrfStruct *Srf, CagdRType OffsetDist)


Description:

Given a surface and an offset amount OffsetDist, returns an approximation to the offset surface by offseting the control mesh in the normal direction.

Parameters:

Srf: To approximate its offset surface with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.


Returned Value:

CagdSrfStruct *: An approximation to the offset surface.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfSubdivOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbSrfRtnlMult

(symb_lib/symbolic.c:1129)

Prototype:

  CagdSrfStruct *SymbSrfRtnlMult(CagdSrfStruct *Srf1X,
                                 CagdSrfStruct *Srf1W,
                                 CagdSrfStruct *Srf2X,
                                 CagdSrfStruct *Srf2W,
                                 CagdBType OperationAdd)


Description:

Given two surfaces - multiply them using the quotient product rule: 
 X = X1 W2 +/- X2 W1

All provided surfaces are assumed to be non rational scalar surfaces. Returned is a non rational scalar surface (CAGD_PT_E1_TYPE).

Parameters:

Srf1X: Numerator of first surface.
Srf1W: Denominator of first surface.
Srf2X: Numerator of second surface.
Srf2W: Denominator of second surface.
OperationAdd: TRUE for addition, FALSE for subtraction.


Returned Value:

CagdSrfStruct *: The result of Srf1X Srf2W +/- Srf2X Srf1W.


See Also:

SymbSrfDotProd SymbSrfVecDotProd SymbSrfScalarScale SymbSrfMultScalar SymbSrfInvert

Keywords:

product symbolic computation

SymbSrfScalarScale

(symb_lib/symbolic.c:867)

Prototype:

  CagdSrfStruct *SymbSrfScalarScale(CagdSrfStruct *Srf, CagdRType Scale)


Description:

Given a surface, scale it by Scale.

Parameters:

Srf: A surface to scale by magnitude Scale.
Scale: Scaling factor.


Returned Value:

CagdSrfStruct *: A surfaces scaled by Scale compared to Srf.


See Also:

SymbSrfDotProd SymbSrfVecDotProd SymbSrfMult SymbSrfMultScalar SymbSrfInvert SymbSrfCrossProd

Keywords:

scaling symbolic computation

SymbSrfSplitScalar

(symb_lib/symbolic.c:1510)

Prototype:

  void SymbSrfSplitScalar(CagdSrfStruct *Srf,
                          CagdSrfStruct **SrfW,
                          CagdSrfStruct **SrfX,
                          CagdSrfStruct **SrfY,
                          CagdSrfStruct **SrfZ)


Description:

Given a surface splits it to its scalar component surfaces. Ignores all dimensions beyond the third, Z, dimension.

Parameters:

Srf: Surface to split.
SrfW: The weight component of Srf, if have any.
SrfX: The X component of Srf.
SrfY: The Y component of Srf, if have any.
SrfZ: The Z component of Srf, if have any.


Returned Value:

void


See Also:

SymbSrfMergeScalar SymbCrvSplitScalar

Keywords:

split symbolic computation

SymbSrfSub

(symb_lib/symbolic.c:756)

Prototype:

  CagdSrfStruct *SymbSrfSub(CagdSrfStruct *Srf1, CagdSrfStruct *Srf2)


Description:

Given two surfaces - subtract them coordinatewise. The two surfaces are promoted to same point type before the multiplication can take place. Furthermore, order and continuity are matched as well.

Parameters:

Srf1, Srf2: Two surface to subtract coordinatewise.


Returned Value:

CagdSrfStruct *: The difference of Srf1 - Srf2 coordinatewise.


See Also:

SymbSrfAdd SymbMeshAddSub SymbSrfMult

Keywords:

subtraction symbolic computation

SymbSrfSubdivOffset

(symb_lib/offset.c:355)

Prototype:

  CagdSrfStruct *SymbSrfSubdivOffset(CagdSrfStruct *Srf,
                                     CagdRType OffsetDist,
                                     CagdRType Tolerance)


Description:

Given a surface and an offset amount OffsetDist, returns an approximation to the offset surface by offseting the control mesh in the normal direction. If resulting offset is not satisfying the required tolerance the surface is subdivided and the algorithm recurses on both parts.

Parameters:

Srf: To approximate its offset surface with distance OffsetDist.
OffsetDist: Amount of offset. Negative denotes other offset direction.
Tolerance: Accuracy control.


Returned Value:

CagdSrfStruct *: An approximation to the offset surface, to within Tolerance.


See Also:

SymbCrvOffset SymbCrvSubdivOffset SymbSrfOffset SymbCrvAdapOffset SymbCrvAdapOffsetTrim SymbCrvLeastSquarOffset SymbCrvMatchingOffset

Keywords:

offset

SymbSrfVecDotProd

(symb_lib/symbolic.c:960)

Prototype:

  CagdSrfStruct *SymbSrfVecDotProd(CagdSrfStruct *Srf, CagdVType Vec)


Description:

Given a surface and a vector - computes their dot product. Returned surface is a scalar surface representing the dot product.

Parameters:

Srf: Curve to multiply and compute a dot product for.
Vec: Vector to project Srf onto.


Returned Value:

CagdSrfStruct *: A scalar surface representing the dot product of Srf . Vec.


See Also:

SymbSrfDotProd SymbSrfMult SymbSrfScalarScale SymbSrfMultScalar SymbSrfInvert SymbSrfCrossProd

Keywords:

product dot product symbolic computation

SymbTwoCrvsMorphing

(symb_lib/morphing.c:53)

Prototype:

  CagdCrvStruct *SymbTwoCrvsMorphing(CagdCrvStruct *Crv1,
                                     CagdCrvStruct *Crv2,
                                     CagdRType Blend)


Description:

Given two compatible curves (See function CagdmakeCrvsCompatible), computes a convex blend between them according to Blend which must be between zero and one. Returned is the new blended curve.

Parameters:

Crv1, Crv2: The two curves to blend.
Blend: A parameter between zero and one


Returned Value:

CagdCrvStruct *: Crv2 * Blend + Crv1 * (1 - Blend).


Keywords:

morphing

SymbTwoCrvsMorphingCornerCut

(symb_lib/morphing.c:117)

Prototype:

  CagdCrvStruct *SymbTwoCrvsMorphingCornerCut(CagdCrvStruct *Crv1,
                                              CagdCrvStruct *Crv2,
                                              CagdRType MinDist,
                                              CagdBType SameLength,
                                              CagdBType FilterTangencies)


Description:

Given two compatible curves (See function CagdMakeCrvsCompatible), computes a morph between them using corner cutting approach. Returned is the new blended curve.

Parameters:

Crv1, Crv2: The two curves to blend.
MinDist: Minimal maximum distance between adjacent curves to make sure motion is visible. The curves will move at most twice that much in their maximal distance (roughly).
SameLength: If TRUE, length of curves is preserved, otherwise BBOX is.
FilterTangenices: f TRUE, attempt is made to eliminate the intermediate line representation.


Returned Value:

CagdCrvStruct *: The blended curve.


Keywords:

morphing

SymbTwoCrvsMorphingMultiRes

(symb_lib/morphing.c:295)

Prototype:

  CagdCrvStruct *SymbTwoCrvsMorphingMultiRes(CagdCrvStruct *Crv1,
                                             CagdCrvStruct *Crv2,
                                             CagdRType BlendStep)


Description:

Given two compatible curves (See function CagdMakeCrvsCompatible), computes a morph between them using multiresolution decomposition. Returned is a list of new blended curves.

Parameters:

Crv1, Crv2: The two curves to blend.
BlendStep: A step size of the blending.


Returned Value:

CagdCrvStruct *: A list of blended curves.


Keywords:

morphing

SymbTwoSrfsMorphing

(symb_lib/morphing.c:727)

Prototype:

  CagdSrfStruct *SymbTwoSrfsMorphing(CagdSrfStruct *Srf1,
                                     CagdSrfStruct *Srf2,
                                     CagdRType Blend)


Description:

Given two compatible surfaces (See function CagdmakeSrfsCompatible), computes a convex blend between them according to Blend which must be between zero and one. Returned is the new blended surface.

Parameters:

Srf1, Srf2: The two surfaces to blend.
Blend: A parameter between zero and one


Returned Value:

CagdSrfStruct *: Srf2 * Blend + Srf1 * (1 - Blend).


Keywords:

morphing

SymvCrvCrvInter

(symb_lib/distance.c:425)

Prototype:

  CagdPtStruct *SymbCrvCrvInter(CagdCrvStruct *Crv1,
                                CagdCrvStruct *Crv2,
                                CagdRType CCIEpsilon,
                                CagdBType SelfInter)


Description:

Computes the intersection points of two planar curves, in the XY plane

Parameters:

Crv1, Crv2: The two curves to intersect.
CCIEpsilon: Tolerance of computation.
SelfInter: If TRUE, needs to handle a curve against itself detecting self intersections in Crv1 (== Crv2).


Returned Value:

CagdPtStruct *: List of intersection points. Each point holds the intersection location in Crv1 as first coefficient and intersection location in Crv2 as first coefficient.


See Also:

SymbSrfDistCrvCrv SymbSrfDistFindPoints

Keywords: