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gen_contour_nurbs_xldT_gen_contour_nurbs_xldGenContourNurbsXldGenContourNurbsXldgen_contour_nurbs_xld (算子)

名称

gen_contour_nurbs_xldT_gen_contour_nurbs_xldGenContourNurbsXldGenContourNurbsXldgen_contour_nurbs_xld — 将 NURBS 曲线变换为 XLD 轮廓。

签名

gen_contour_nurbs_xld( : Contour : Rows, Cols, Knots, Weights, Degree, MaxError, MaxDistance : )

Herror T_gen_contour_nurbs_xld(Hobject* Contour, const Htuple Rows, const Htuple Cols, const Htuple Knots, const Htuple Weights, const Htuple Degree, const Htuple MaxError, const Htuple MaxDistance)

void GenContourNurbsXld(HObject* Contour, const HTuple& Rows, const HTuple& Cols, const HTuple& Knots, const HTuple& Weights, const HTuple& Degree, const HTuple& MaxError, const HTuple& MaxDistance)

void HXLDCont::GenContourNurbsXld(const HTuple& Rows, const HTuple& Cols, const HTuple& Knots, const HTuple& Weights, Hlong Degree, const HTuple& MaxError, const HTuple& MaxDistance)

void HXLDCont::GenContourNurbsXld(const HTuple& Rows, const HTuple& Cols, const HString& Knots, const HString& Weights, Hlong Degree, double MaxError, double MaxDistance)

void HXLDCont::GenContourNurbsXld(const HTuple& Rows, const HTuple& Cols, const char* Knots, const char* Weights, Hlong Degree, double MaxError, double MaxDistance)

void HXLDCont::GenContourNurbsXld(const HTuple& Rows, const HTuple& Cols, const wchar_t* Knots, const wchar_t* Weights, Hlong Degree, double MaxError, double MaxDistance)   ( Windows only)

static void HOperatorSet.GenContourNurbsXld(out HObject contour, HTuple rows, HTuple cols, HTuple knots, HTuple weights, HTuple degree, HTuple maxError, HTuple maxDistance)

void HXLDCont.GenContourNurbsXld(HTuple rows, HTuple cols, HTuple knots, HTuple weights, int degree, HTuple maxError, HTuple maxDistance)

void HXLDCont.GenContourNurbsXld(HTuple rows, HTuple cols, string knots, string weights, int degree, double maxError, double maxDistance)

def gen_contour_nurbs_xld(rows: Sequence[float], cols: Sequence[float], knots: MaybeSequence[Union[str, float]], weights: MaybeSequence[Union[str, float]], degree: int, max_error: Union[float, str], max_distance: Union[float, str]) -> HObject

描述

gen_contour_nurbs_xldgen_contour_nurbs_xldGenContourNurbsXldGenContourNurbsXldGenContourNurbsXldgen_contour_nurbs_xld generates an XLD ContourContourContourContourcontourcontour that approximates a NURBS curve (non-uniform rational B-Spline curve). The NURBS curve is specified by its DegreeDegreeDegreeDegreedegreedegree, a control polygon (via RowsRowsRowsRowsrowsrows and ColsColsColsColscolscols), a WeightsWeightsWeightsWeightsweightsweights vector and a KnotsKnotsKnotsKnotsknotsknots vector.

The DegreeDegreeDegreeDegreedegreedegree of the curve determines the grade of differentiability of the curve. The curve lies within the convex hull of its control polygon (RowsRowsRowsRowsrowsrows,ColsColsColsColscolscols). The weights in WeightsWeightsWeightsWeightsweightsweights determine how much the curve is attracted by the individual control points (RowsRowsRowsRowsrowsrows,ColsColsColsColscolscols). A WeightsWeightsWeightsWeightsweightsweights vector with equal weights for all control points is generated if 'auto'"auto""auto""auto""auto""auto" is chosen. The KnotsKnotsKnotsKnotsknotsknots vector describes the domain of the curve. Typically, this parameter can be set to 'auto'"auto""auto""auto""auto""auto".

The accuracy of the generated ContourContourContourContourcontourcontour depends on the two parameters MaxDistanceMaxDistanceMaxDistanceMaxDistancemaxDistancemax_distance and MaxErrorMaxErrorMaxErrorMaxErrormaxErrormax_error. MaxDistanceMaxDistanceMaxDistanceMaxDistancemaxDistancemax_distance limits the maximum distance of two subsequent ContourContourContourContourcontourcontour points. The maximum distance between the generated ContourContourContourContourcontourcontour and the actual NURBS curve is limited to MaxErrorMaxErrorMaxErrorMaxErrormaxErrormax_error. By default the approximation must fulfill both constraints, but it is possible to set one of these parameters to 'omit'"omit""omit""omit""omit""omit". The lower MaxErrorMaxErrorMaxErrorMaxErrormaxErrormax_error and MaxDistanceMaxDistanceMaxDistanceMaxDistancemaxDistancemax_distance are chosen the better is the approximation of the curve. Note that all ContourContourContourContourcontourcontour points lie exactly on the curve (except for numerical inaccuracies).

Definition

A NURBS curve of degree is given by The basis functions are defined by Thus, each NURBS curve is determined by its DegreeDegreeDegreeDegreedegreedegree , its control Polygon (RowsRowsRowsRowsrowsrows and ColsColsColsColscolscols), its weight vector (WeightsWeightsWeightsWeightsweightsweights), and its knot vector (KnotsKnotsKnotsKnotsknotsknots).

The grade of differentiability of the curve is set via the degree . At least control points are required to form a valid curve. The knot vector describes the domain of the curve. Its length must be and its entries must be monotonically increasing. Every entry stands for a knot between the curve segments and . Each curve segment lies within the convex hull of the control points . For every curve segment of length zero, the differentiability at knot decreases. The number of occurrences of each knot in the knot vector is called multiplicity. The maximum multiplicity of one knot is . Only the start and the end point's multiplicity can be (which in fact is the case for most curves, because in this case start and end point of the curve correspond to the first respectively last point of the control polygon). If start and/or end point do not have full multiplicity, the domain of the curve is restricted to . The weights determine the influence of the individual control points on the curve.

Closed Curves: If start and end point are equal ( ) and KnotsKnotsKnotsKnotsknotsknots is set to 'auto'"auto""auto""auto""auto""auto", the curve is closed automatically such that all knots feature multiplicity one. Note that in this case the length of WeightsWeightsWeightsWeightsweightsweights is required to be 。

执行信息

参数

ContourContourContourContourcontourcontour (输出对象)  xld_cont → objectHXLDContHObjectHXLDContHobject *

The contour that approximates the NURBS curve.

RowsRowsRowsRowsrowsrows (输入控制)  coordinates.y-array → HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Row coordinates of the control polygon.

元素数量： Rows == Cols && Rows >= Degree + 1

ColsColsColsColscolscols (输入控制)  coordinates.x-array → HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Column coordinates of the control polygon.

元素数量： Cols == Rows && Cols >= Degree + 1

KnotsKnotsKnotsKnotsknotsknots (输入控制)  string(-array) → HTupleMaybeSequence[Union[str, float]]HTupleHtuple (string / real) (string / double) (HString / double) (char* / double)

The knot vector 。

默认值： 'auto' "auto" "auto" "auto" "auto" "auto"

建议值： 'auto'"auto""auto""auto""auto""auto"

WeightsWeightsWeightsWeightsweightsweights (输入控制)  string(-array) → HTupleMaybeSequence[Union[str, float]]HTupleHtuple (string / real) (string / double) (HString / double) (char* / double)

The weight vector 。

元素数量： Weights == Rows

默认值： 'auto' "auto" "auto" "auto" "auto" "auto"

建议值： 'auto'"auto""auto""auto""auto""auto"

限制： Weights > 0.0

DegreeDegreeDegreeDegreedegreedegree (输入控制)  integer → HTupleintHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

The degree of the NURBS curve.

默认值： 3

建议值： 2, 3, 4, 5

限制： Degree >= 2

MaxErrorMaxErrorMaxErrorMaxErrormaxErrormax_error (输入控制)  real → HTupleUnion[float, str]HTupleHtuple (real / string) (double / string) (double / HString) (double / char*)

Maximum distance between the NURBS curve and its approximation.

默认值： 1.0

建议值： 'omit'"omit""omit""omit""omit""omit", 1.0, 2.0, 3.0, 4.0, 5.0

限制： MaxError > 0.0

MaxDistanceMaxDistanceMaxDistanceMaxDistancemaxDistancemax_distance (输入控制)  real → HTupleUnion[float, str]HTupleHtuple (real / string) (double / string) (double / HString) (double / char*)

Maximum distance between two subsequent ContourContourContourContourcontourcontour points.

默认值： 5.0

建议值： 'omit'"omit""omit""omit""omit""omit", 1.0, 2.0, 3.0, 4.0, 5.0

限制： MaxDistance > 0.0

示例（HDevelop）

* use a polygon XLD contour as control polygon and approximate
* the NURBS curve as contour

get_contour_xld(Polygon, Row, Col)
gen_contour_nurbs_xld(NURBSContour, Row, Col, 'auto', 'auto', 3, 1.0, 10.0)

可能的前趋

gen_nurbs_interpgen_nurbs_interpGenNurbsInterpGenNurbsInterpGenNurbsInterpgen_nurbs_interp

可能的后继

gen_polygons_xldgen_polygons_xldGenPolygonsXldGenPolygonsXldGenPolygonsXldgen_polygons_xld

参考文献

L. Piegl, W. Tiller: ”The NURBS Book”, 2nd Edition, Springer, 1997.

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基础

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