Creates a three-dimensional point behavior. The location of the point is calculated by adding the corresponding coordinates of the given point and vector behaviors.
public static Point3Bvr add(
Point3Bvr pt,
Vector3Bvr vec
);
Returns the Point3Bvr object.
Creates a Point3Bvr behavior based on a B-spline function. The function depends on the control elements, the knot vector, the mathematical degree, and the weights of the control elements (these are optional).
A B-spline function without weights is piecewise polynomial and with weights is piecewise rational (the quotient of two polynomials). It requires that:
numberOfControlElements = numberOfKnots - degree + 1
The control elements define the approximate direction and shape of the function. The knots represent junction values, in parameter space, between the connected polynomial parts.
Given a degree d and a number of knots k, the function is valid in the range knotd to knotk-d+1, and is otherwise undefined. For example, for a degree 2 curve, the valid range is from the second knot to the next to the last knot, inclusive.
The returned Point3Bvr is the traversal of the spline function according to the evaluation parameter. The evaluation parameter is a NumberBvr that must be in the valid range of the spline, which is [knotd, knotk-d+1]. Any values outside this range are automatically clamped to the end values.
public static Point3Bvr bSpline(
int degree,
NumberBvr[] knots,
Point3Bvr[] control_elements,
NumberBvr[] weights,
NumberBvr evaluation
);
Returns the Point3Bvr object.
Creates a three-dimensional vector behavior of the instantaneous derivative (rate of change) of the given point behavior. For example, a constant yields a constant derivative of [0 0 0], and point3(time, 0) (without additional time substitutions) yields a constant derivative of [1 0 0].
public static Vector3Bvr derivative(
Point3Bvr pt
);
Returns the Vector3Bvr object.
Creates a number behavior representing the distance between two point behaviors.
public static NumberBvr distance(
Point3Bvr p1,
Point3Bvr p2
);
Returns the NumberBvr object.
Creates a number behavior representing the square of the distance between two point behaviors. This is the same as the distance method except that the distance is squared.
public static NumberBvr distanceSquared(
Point3Bvr p1,
Point3Bvr p2
);
Returns the NumberBvr object.
This method is slightly more efficient than the distance method.
Creates a three-dimensional point behavior. The location of the point is given in Cartesian coordinates.
public static Point3Bvr point3(
NumberBvr x,
NumberBvr y,
NumberBvr z
);
Returns the Point3Bvr object.
Creates a three-dimensional point behavior. The location of the point is given in spherical coordinates.
public static Point3Bvr point3Spherical(
NumberBvr XYangle,
NumberBvr YZangle,
NumberBvr length
);
Returns the Point3Bvr object.
The following table correlates Cartesian coordinates with polar coordinates:
Cartesian | XYangle | YZangle | Length | |
Coordinates | ||||
[0 0 0] | X | X | 0 | |
[d 0 0] | pi/2 | 0 | d | |
[-d 0 0] | -pi/2 | 0 | d | X = Don't Care |
[0 d 0] | X | pi/2 | d | |
[0 -d 0] | X | -pi/2 | d | |
[0 0 d] | 0 | 0 | d | |
[0 0 -d] | pi | 0 | d |
Creates a three-dimensional vector behavior. The coordinate values of the vector are calculated by subtracting the coordinates of p3 from the corresponding coordinates of p1.
public static Vector3Bvr sub(
Point3Bvr p1,
Point3Bvr p2
);
Returns the Vector3Bvr object.
Creates a three-dimensional point behavior. The location of the point is calculated by subtracting the coordinates of the given vector behavior from the corresponding coordinates of the given point behavior.
public static Point3Bvr sub(
Point3Bvr pt,
Vector3Bvr vec
);
Returns the Point3Bvr object.
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