DAStatics Functions Relevant to DAPoint3 Objects
AddPoint3Vector Creates a DAPoint3 object. The location of the point is calculated by adding the corresponding coordinates of the given point and vector behaviors. DerivativePoint3 Creates a DAVector3 object of the instantaneous derivative (rate of change) of the given point. DistancePoint3 Creates a DANumber representing the distance between two points. DistanceSquaredPoint3 Creates a DANumber object representing the square of the distance between two points. Point3 Creates a DAPoint3 object. The location of the point is given in Cartesian coordinates. Same as Point3Anim except that x, y, and z are nonanimated numbers (doubles). Point3Anim Creates a DAPoint3 object. The location of the point is given in Cartesian coordinates. Point3BSpline Creates a DAPoint3 behavior based on a B-spline function. Point3Spherical Creates a DAPoint3 object. The location of the point is given in spherical coordinates. Same as Point3SphericalAnim except that XYangle, YZangle, and length are nonanimated numbers (doubles). Point3SphericalAnim Creates a DAPoint3 object. The location of the point is given in spherical coordinates. SubPoint3 Creates a DAVector3 object. The coordinate values of the vector are calculated by subtracting the coordinates of p3 from the corresponding coordinates of p1. SubPoint3Vector Creates a DAPoint3 object. The location of the point is calculated by subtracting the coordinates of the given vector behavior from the corresponding coordinates of the given point.
AddPoint3Vector
DAStatics Class
Creates a DAPoint3 object. The location of the point is calculated by adding the corresponding coordinates of the given point and vector behaviors.
Syntax
lib.AddPoint3Vector( pt, vec )
Parameters
- pt
- DAPoint3 object.
- vec
- DAVector3 object.
Return Value
Returns the DAPoint3 object.
See Also
DerivativePoint3
DAStatics Class
Creates a DAVector3 object of the instantaneous derivative (rate of change) of the given point. 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].
Syntax
lib.DerivativePoint3( pt )
Parameters
- pt
- DAPoint3 object.
Return Value
Returns the DAVector3 object.
DistancePoint3
DAStatics Class
Creates a DANumber representing the distance between two points.
Syntax
lib.DistancePoint3( p1, p2 )
Parameters
- p1 and p3
- DAPoint3 objects.
Return Value
Returns the DANumber object.
See Also
DistanceSquaredPoint3
DAStatics Class
Creates a DANumber object representing the square of the distance between two points. This is the same as the DistancePoint3 function except that the distance is squared.
Syntax
lib.DistanceSquaredPoint3( p1, p2 )
Parameters
- p1 and p2
- DAPoint3 objects.
Return Value
Returns the DANumber object.
See Also
Point3
DAStatics Class
Creates a DAPoint3 object. The location of the point is given in Cartesian coordinates. Same as Point3Anim except that x, y, and z are nonanimated numbers (doubles).
Syntax
lib.Point3( x, y, z )
Parameters
- x, y, and z
- Values specifying the coordinates. The x specifies the distance along the x-axis from the origin to the point, y specifies the distance along the y-axis, and z the distance along the z-axis. These are nonanimated numbers (double values).
Return Value
Returns the DAPoint3 object.
Point3Anim
DAStatics Class
Creates a DAPoint3 object. The location of the point is given in Cartesian coordinates.
Syntax
lib.Point3Anim( x, y, z )
Parameters
- x, y, and z
- DANumber objects, specifying the coordinate values. The x specifies the distance along the x-axis from the origin to the point, y specifies the distance along the y-axis, and z the distance along the z-axis. These must be animated numbers.
Return Value
Returns the DAPoint3 object.
See Also
Point3BSpline
DAStatics Class
Creates a DAPoint3 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).
Syntax
lib.Point3BSpline( degree, knots, control_elements, weights, evaluation )
Parameters
- degree
- Number (long) representing the mathematical degree of the B-spline to evaluate. Must be 1, 2, or 3.
- knots
- Array (variant) of DANumber objects representing the knots used to calculate the B-spline.
- control_elements
- Array (variant) of DAPoint3 objects representing the control elements used to calculate the B-spline.
- weights
- Array (variant) of DANumber objects representing the weights used to calculate the B-spline. There must be the same number of weights as control elements. For nonrational B-splines, the value of weights is null.
- evaluation
- DANumber object that controls the spline evaluation.
Return Value
Returns the DAPoint3 object.
Remarks
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 DAPoint3 is the traversal of the spline function according to the evaluation parameter. The evaluation parameter is a DANumber 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.
Point3Spherical
DAStatics Class
Creates a DAPoint3 object. The location of the point is given in spherical coordinates. Same as Point3SphericalAnim except that XYangle, YZangle, and length are nonanimated numbers (doubles).
Syntax
lib.Point3Spherical( XYangle, YZangle, length )
Parameters
- XYangle
- A double value indicating the counterclockwise XY angle, in radians, of the point about the positive y-ray. The angle begins at the positive z-ray, so that [0 0 1] has a theta of 0, and [1 0 0] has a theta of pi/2. This is a nonanimated number.
- YZangle
- A double value indicating the counterclockwise elevation angle, in radians, of the point above the XZ-plane. A YZangle of pi/2 means the point is straight up (on the positive y-ray), and a YZangle of –pi/2 is straight down (on the negative y-ray). This is a nonanimated number.
- length
- A double value indicating the distance of the point from the origin. This is a nonanimated number.
Return Value
Returns the DAPoint3 object.
Remarks
The following table correlates Cartesian coordinates with polar coordinates (X means "Don't Care").
Cartesian coordinates XYangle YZangle length [0 0 0] X X 0 [d 0 0] pi/2 0 d [-d 0 0] –pi/2 0 d [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
Point3SphericalAnim
DAStatics Class
Creates a DAPoint3 object. The location of the point is given in spherical coordinates.
Syntax
lib.Point3SphericalAnim( XYangle, YZangle, length )
Parameters
- XYangle
- DANumber object of the counterclockwise XY angle, in radians, of the point about the positive y-ray. The angle begins at the positive z-ray, so that [0 0 1] has a theta of 0, and [1 0 0] has a theta of pi/2. This must be an animated number.
- YZangle
- DANumber object of the counterclockwise elevation angle, in radians, of the point above the XZ-plane. A YZangle of pi/2 means the point is straight up (on the positive y-ray), and a YZangle of –pi/2 is straight down (on the negative y-ray). This must be an animated number.
- length
- DANumber object of the distance of the point from the origin. This must be an animated number.
Return Value
Returns the DAPoint3 object.
Remarks
The following table correlates Cartesian coordinates with polar coordinates (X means "Don't Care").
Cartesian coordinates XYangle YZangle length [0 0 0] X X 0 [d 0 0] pi/2 0 d [-d 0 0] –pi/2 0 d [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
See Also
SubPoint3
DAStatics Class
Creates a DAVector3 object. The coordinate values of the vector are calculated by subtracting the coordinates of p2 from the corresponding coordinates of p1.
Syntax
lib.SubPoint3( p1, p2 )
Parameters
- p1 and p2
- DAPoint3 objects.
Return Value
Returns the DAVector3 object.
SubPoint3Vector
DAStatics Class
Creates a DAPoint3 object. The location of the point is calculated by subtracting the coordinates of the given vector behavior from the corresponding coordinates of the given point.
Syntax
lib.SubPoint3Vector( pt, vec )
Parameters
- pt
- DAPoint3 object.
- vec
- DAVector3 object.
Return Value
Returns the DAPoint3 object.
See Also
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