BSplineSurface

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new BSplineSurface(controlPoints, knotsU, knotsV, [bits])

Augments: Surface

A surface evaluator object for a B-spline (basis spline) surface, whose edges are made up of B-spline curves. For more on B-spline curves, see the constructor for BSplineCurve.

Parameters

Examples

Together with 'convertToHomogen' given in the BSplineCurve documentation, the following function can be used to convert an array of arrays of control points, each consisting of conventional coordinates and a weight, to homogeneous coordinates. For example, the single-control point array '[[[2, 3, 4, 0.1]]]' becomes '[[[0.2, 0.3, 0.4, 0.1]]]'; the return value can then be used in the BSplineSurface constructor to create a rational B-Spline surface.

function convertSurfaceToHomogen(cp) {
var ret = [];
for(var i = 0; i < cp.length; i++) {
ret.push(convertToHomogen(cp[i]));
}
return ret;
};

Methods

BSplineSurface#bitangent(u, v)

Finds the bitangent vector at the given point on the surface.

Parameters

Return Value

An array giving the bitangent vector. It will have as many elements as a control point (or one fewer if DIVIDE_BIT is set), as specified in the constructor. (Type: Array.<number>)

(static) BSplineSurface.clamped(controlPoints, [degreeU], [degreeV], [bits])

Creates a B-spline surface with uniform knots, except that the surface's edges lie on the edges of the control point array.

Parameters

Return Value

Return value. The first knot of the curve will be 0 and the last knot will be 1. (Type: BSplineSurface)

BSplineSurface#endPoints()

Returns the starting and ending U and V coordinates of this surface. This method calls the evaluator's endPoints method if it implements it; otherwise, returns [0, 1, 0, 1]

Return Value

A four-element array. The first and second elements are the starting and ending U coordinates, respectively, of the surface, and the third and fourth elements are its starting and ending V coordinates. Returns [0, 1, 0, 1] if the evaluator doesn't implement an endPoints method.

BSplineSurface#evaluate(u, v)

Evaluates the surface function based on a point in a B-spline surface.

Parameters

Return Value

An array of the result of the evaluation. It will have as many elements as a control point (or one fewer if DIVIDE_BIT is set), as specified in the constructor. (Type: Array.<number>)

(static) BSplineSurface.fromBezierSurface(controlPoints, [bits])

Creates a B-spline surface from the control points of a Bézier surface.

Parameters

Return Value

Return value. (Type: BSplineSurface)

BSplineSurface#getControlPoints()

Gets a reference to the array of control point arrays used in this surface object.

Return Value

An object described in the constructor to BSplineCurve. (Type: Array.<Array.<number>>)

BSplineSurface#getKnots()

Gets a reference to the array of knot vectors used in this curve object.

Return Value

An object described in the constructor to BSplineSurface. (Type: Array.<Array.<number>>)

BSplineSurface#gradient(u, v)

Finds an approximate gradient vector of this surface at the given U and V coordinates.

The implementation in Surface calls the evaluator's gradient method if it implements it; otherwise uses the surface's tangent and bitangent vectors to implement the gradient (however, this approach is generally only meaningful for a surface in three-dimensional space).

The gradient is a vector pointing up and away from the surface. If the evaluator describes a regular three-dimensional surface (usually a continuous, unbroken surface such as a sphere, an open cylinder, or a disk rotated in three dimensions), this can be the cross product of the tangent vector and bitangent vector, in that order. The gradient returned by this method should not be "normalized" to a unit vector.

Parameters

Return Value

An array describing a gradient vector. It should have at least as many elements as the number of dimensions of the underlying surface. (Type: Array.<number>)

Examples

The following example is a surface evaluator object for a parametric surface with a gradient method. To illustrate how the gradient method is derived from the vector calculation method, that method is also given below. To derive the normal calculation, first look at the vector function:

F(u, v) = (cos(u), sin(u), sin(u)*cos(v))

Then, find the partial derivatives with respect to u and to v:

∂F/∂u = (-sin(u), cos(u), cos(u)*cos(v))
∂F/∂v = (0, 0, -sin(v)*sin(u))

Next, take their cross product:

∇F(u, v) = (-sin(v)*cos(u)*sin(u), -sin(v)*sin(u)*sin(u), 0)

The result is the gradient, which will point up and away from the surface.

var surface=new Surface({"evaluate":function(u,v) {
"use strict";
return [Math.cos(u),Math.sin(u),Math.sin(u)*Math.cos(v)];
},
"gradient":function(u,v) {
"use strict";
return [
Math.cos(u)*-Math.sin(v)*Math.sin(u),
Math.sin(u)*-Math.sin(v)*Math.sin(u),
0];
}})

BSplineSurface#normal(u, v)

Convenience method for finding an approximate normal vector of this surface at the given U and V coordinates. The normal vector is the same as the gradient vector, but "normalized" to a unit vector.

Parameters

Return Value

An array describing a normal vector. It should have at least as many elements as the number of dimensions of the underlying surface. (Type: Array.<number>)

BSplineSurface#tangent(u, v)

Finds the tangent vector at the given point on the surface.

Parameters

Return Value

An array giving the tangent vector. It will have as many elements as a control point (or one fewer if DIVIDE_BIT is set), as specified in the constructor. (Type: Array.<number>)

(static) BSplineSurface.uniform(controlPoints, [degreeU], [degreeV], [bits])

Creates a B-spline surface with uniform knots.

Parameters

Return Value

Return value. The first knot of the curve will be 0 and the last knot will be 1. (Type: BSplineSurface)

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