Describes a B-Spline surface in 3D space Returns the degree of this B-Spline surface in the u parametric direction. Returns the degree of this B-Spline surface in the v parametric direction. Returns the value of the maximum polynomial degree of any B-Spline surface surface in either parametric directions. This value is 25. Returns the number of poles of this B-Spline surface in the u parametric direction. Returns the number of poles of this B-Spline surface in the v parametric direction. Returns the number of knots of this B-Spline surface in the u parametric direction. Returns the number of knots of this B-Spline surface in the v parametric direction. Returns the index in the knot array associated with the u parametric direction, which corresponds to the first parameter of this B-Spline surface in the specified parametric direction. The isoparametric curves corresponding to these values are the boundary curves of this surface. Note: The index does not correspond to the first knot of the surface in the specified parametric direction unless the multiplicity of the first knot is equal to Degree + 1, where Degree is the degree of this surface in the corresponding parametric direction. Returns the index in the knot array associated with the u parametric direction, which corresponds to the last parameter of this B-Spline surface in the specified parametric direction. The isoparametric curves corresponding to these values are the boundary curves of this surface. Note: The index does not correspond to the first knot of the surface in the specified parametric direction unless the multiplicity of the last knot is equal to Degree + 1, where Degree is the degree of this surface in the corresponding parametric direction. Returns the index in the knot array associated with the v parametric direction, which corresponds to the first parameter of this B-Spline surface in the specified parametric direction. The isoparametric curves corresponding to these values are the boundary curves of this surface. Note: The index does not correspond to the first knot of the surface in the specified parametric direction unless the multiplicity of the first knot is equal to Degree + 1, where Degree is the degree of this surface in the corresponding parametric direction. Returns the index in the knot array associated with the v parametric direction, which corresponds to the last parameter of this B-Spline surface in the specified parametric direction. The isoparametric curves corresponding to these values are the boundary curves of this surface. Note: The index does not correspond to the first knot of the surface in the specified parametric direction unless the multiplicity of the last knot is equal to Degree + 1, where Degree is the degree of this surface in the corresponding parametric direction. Returns the knots sequence of this B-Spline surface in the u direction. Returns the knots sequence of this B-Spline surface in the v direction. Returns the parametric bounds (U1, U2, V1, V2) of this B-Spline surface. Returns false if the equation of this B-Spline surface is polynomial (e.g. non-rational) in the u or v parametric direction. In other words, returns false if for each row of poles, the associated weights are identical Returns false if the equation of this B-Spline surface is polynomial (e.g. non-rational) in the u or v parametric direction. In other words, returns false if for each column of poles, the associated weights are identical Returns true if this surface is periodic in the u parametric direction. Returns true if this surface is periodic in the v parametric direction. Checks if this surface is closed in the u parametric direction. Returns true if, in the table of poles the first row and the last row are identical. Checks if this surface is closed in the v parametric direction. Returns true if, in the table of poles the first column and the last column are identical. increase(Int=UDegree, int=VDegree) Increases the degrees of this B-Spline surface to UDegree and VDegree in the u and v parametric directions respectively. As a result, the tables of poles, weights and multiplicities are modified. The tables of knots is not changed. Note: Nothing is done if the given degree is less than or equal to the current degree in the corresponding parametric direction. Increases the multiplicity in the u direction. Increases the multiplicity in the v direction. Increment the multiplicity in the u direction Increment the multiplicity in the v direction insertUKnote(float U, int Index, float Tolerance) - Insert or overide a knot insertUKnote(List of float U, List of float Mult, float Tolerance) - Inserts knots. insertUKnote(float V, int Index, float Tolerance) - Insert or overide a knot. insertUKnote(List of float V, List of float Mult, float Tolerance) - Inserts knots. Reduces to M the multiplicity of the knot of index Index in the given parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance 'smoothes' the surface. Reduces to M the multiplicity of the knot of index Index in the given parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance 'smoothes' the surface. Modifies this B-Spline surface by segmenting it between U1 and U2 in the u parametric direction and between V1 and V2 in the v parametric direction. Any of these values can be outside the bounds of this surface, but U2 must be greater than U1 and V2 must be greater than V1. All the data structure tables of this B-Spline surface are modified but the knots located between U1 and U2 in the u parametric direction, and between V1 and V2 in the v parametric direction are retained. The degree of the surface in each parametric direction is not modified. Modifies this B-Spline surface by assigning the value K to the knot of index UIndex of the knots table corresponding to the u parametric direction. This modification remains relatively local, since K must lie between the values of the knots which frame the modified knot. You can also increase the multiplicity of the modified knot to M. Note however that it is not possible to decrease the multiplicity of a knot with this function. Modifies this B-Spline surface by assigning the value K to the knot of index VIndex of the knots table corresponding to the v parametric direction. This modification remains relatively local, since K must lie between the values of the knots which frame the modified knot. You can also increase the multiplicity of the modified knot to M. Note however that it is not possible to decrease the multiplicity of a knot with this function. Returns, for this B-Spline surface, in the u parametric direction the knot of index UIndex of the knots table. Returns, for this B-Spline surface, in the v parametric direction the knot of index VIndex of the knots table. Changes all knots of this B-Spline surface in the u parametric direction. The multiplicity of the knots is not modified. Changes all knots of this B-Spline surface in the v parametric direction. The multiplicity of the knots is not modified. Returns, for this B-Spline surface, the knots table in the u parametric direction Returns, for this B-Spline surface, the knots table in the v parametric direction Modifies this B-Spline surface by assigning P to the pole of index (UIndex, VIndex) in the poles table. The second syntax allows you also to change the weight of the modified pole. The weight is set to Weight. This syntax must only be used for rational surfaces. Modifies this B-Spline curve by assigning P to the pole of index Index in the poles table. Modifies this B-Spline surface by assigning values to all or part of the column of poles of index VIndex, of this B-Spline surface. You can also change the weights of the modified poles. The weights are set to the corresponding values of CPoleWeights. These syntaxes must only be used for rational surfaces. Modifies this B-Spline surface by assigning values to all or part of the row of poles of index VIndex, of this B-Spline surface. You can also change the weights of the modified poles. The weights are set to the corresponding values of CPoleWeights. These syntaxes must only be used for rational surfaces. Returns the pole of index (UIndex,VIndex) of this B-Spline surface. Returns the table of poles of this B-Spline surface. Modifies this B-Spline surface by assigning the value Weight to the weight of the pole of index (UIndex, VIndex) in the poles tables of this B-Spline surface. This function must only be used for rational surfaces. Modifies this B-Spline surface by assigning values to all or part of the weights of the column of poles of index VIndex of this B-Spline surface. The modified part of the column of weights is defined by the bounds of the array CPoleWeights. This function must only be used for rational surfaces. Modifies this B-Spline surface by assigning values to all or part of the weights of the row of poles of index UIndex of this B-Spline surface. The modified part of the row of weights is defined by the bounds of the array CPoleWeights. This function must only be used for rational surfaces. Return the weight of the pole of index (UIndex,VIndex) in the poles table for this B-Spline surface. Returns the table of weights of the poles for this B-Spline surface. Returns the table of poles and weights in homogenous ccordinates. Computes two tolerance values for this B-Spline surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are: -- UTolerance in the u parametric direction and -- VTolerance in the v parametric direction. If f(u,v) is the equation of this B-Spline surface, UTolerance and VTolerance guarantee that: |u1 - u0| < UTolerance |v1 - v0| < VTolerance ====> ||f(u1, v1) - f(u2, v2)|| < Tolerance3D Moves the point of parameters (U, V) of this B-Spline surface to P. UIndex1, UIndex2, VIndex1 and VIndex2 are the indexes in the poles table of this B-Spline surface, of the first and last poles which can be moved in each parametric direction. The returned indexes UFirstIndex, ULastIndex, VFirstIndex and VLastIndex are the indexes of the first and last poles effectively modified in each parametric direction. In the event of incompatibility between UIndex1, UIndex2, VIndex1, VIndex2 and the values U and V: -- no change is made to this B-Spline surface, and -- UFirstIndex, ULastIndex, VFirstIndex and VLastIndex are set to null. Changes this B-Spline surface into a non-periodic one in the u parametric direction. If this B-Spline surface is already non-periodic in the given parametric direction, it is not modified. If this B-Spline surface is periodic in the given parametric direction, the boundaries of the surface are not given by the first and last rows (or columns) of poles (because the multiplicity of the first knot and of the last knot in the given parametric direction are not modified, nor are they equal to Degree+1, where Degree is the degree of this B-Spline surface in the given parametric direction). Only the function Segment ensures this property. Note: the poles and knots tables are modified. Changes this B-Spline surface into a non-periodic one in the v parametric direction. If this B-Spline surface is already non-periodic in the given parametric direction, it is not modified. If this B-Spline surface is periodic in the given parametric direction, the boundaries of the surface are not given by the first and last rows (or columns) of poles (because the multiplicity of the first knot and of the last knot in the given parametric direction are not modified, nor are they equal to Degree+1, where Degree is the degree of this B-Spline surface in the given parametric direction). Only the function Segment ensures this property. Note: the poles and knots tables are modified. Modifies this surface to be periodic in the u parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this B-Spline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Modifies this surface to be periodic in the v parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this B-Spline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Assigns the knot of index Index in the knots table in the u parametric direction to be the origin of this periodic B-Spline surface. As a consequence, the knots and poles tables are modified. Assigns the knot of index Index in the knots table in the v parametric direction to be the origin of this periodic B-Spline surface. As a consequence, the knots and poles tables are modified. Returns, for this B-Spline surface, the multiplicity of the knot of index UIndex in the u parametric direction. Returns, for this B-Spline surface, the multiplicity of the knot of index VIndex in the v parametric direction. Returns, for this B-Spline surface, the table of multiplicities in the u parametric direction Returns, for this B-Spline surface, the table of multiplicities in the v parametric direction Exchanges the u and v parametric directions on this B-Spline surface. As a consequence: -- the poles and weights tables are transposed, -- the knots and multiplicities tables are exchanged, -- degrees of continuity and rational, periodic and uniform characteristics are exchanged and -- the orientation of the surface is reversed. Builds the U isoparametric B-Spline curve of this B-Spline surface Builds the V isoparametric B-Spline curve of this B-Spline surface Returns a reparametrized copy of this surface approximate(points, degMin, degMax, continuity, tol) approximate(zPoints, degMin, degMax, continuity, tol, X0, dX, Y0, dY) Replaces this B-Spline surface by approximating a set of points. continuity is an integer between 0 and 3 interpolate(points) interpolate(zpoints, X0, dX, Y0, dY) Replaces this B-Spline surface by interpolating a set of points. The resulting surface is of degree 3 and continuity C2. Arguments: a 2 dimensional array of vectors, that the surface passes through or a 2 dimensional array of floats with the z values, the x starting point X0 (float), the x increment dX (float), the y starting point Y0 and increment dY Builds a B-Spline by a lists of Poles, Mults and Knots arguments: poles (sequence of sequence of Base.Vector), umults, vmults, [uknots, vknots, uperiodic, vperiodic, udegree, vdegree, weights (sequence of sequence of float)]