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DAStatic Functions Relevant to DAPoint3 Objects
DAStatics Class
AddPoint3VectorCreates a DAPoint3 object. The location of the point is calculated by adding the corresponding coordinates of the given point and vector behaviors.
lib.AddPoint3Vector(
pt,
vec
)Parameters
- pt
- A DAPoint3 object.
- vec
- A DAVector3 object.
Return Values
Returns the DAPoint3 object.
See Also
DAStatics Class
DerivativePoint3Creates 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].
lib.DerivativePoint3(
pt
)Parameters
- pt
- A DAPoint3 object.
Return Values
Returns the DAVector3 object.
DAStatics Class
DistancePoint3Creates a DANumber representing the distance between two points.
lib.DistancePoint3(
p1,
p2
)Parameters
- p1 and p3
- The DAPoint3 objects.
Return Values
Returns the DANumber object.
See Also
DAStatics Class
DistanceSquaredPoint3Creates 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.
lib.DistanceSquaredPoint3(
p1,
p2
)Parameters
- p1 and p3
- The DAPoint3 objects.
Return Values
Returns the DANumber object.
See Also
DAStatics Class
Point3AnimCreates a DAPoint3 object. The location of the point is given in Cartesian coordinates.
lib.Point3Anim(
x,
y,
z
)Parameters
- x, y, and z
- The 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 Values
Returns the DAPoint3 object.
See Also
DAStatics Class
Point3Same as Point3Anim except that x, y, and z are non-animated numbers (doubles).
lib.Point3(
x,
y,
z
)DAStatics Class
Point3BSplineCreates 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).
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.
lib.Point3BSpline(
degree,
knots,
control_elements,
weights,
evaluation
)Parameters
- degree
- A number (long) representing the mathematical degree of the B-spline to evaluate. Must be 1, 2, or 3.
- knots
- An array (variant) of DANumber objects representing the knots used to calculate the B-spline.
- control_elements
- An array (variant) of DAPoint3 objects representing the control elements used to calculate the B-spline.
- weights
- An 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 non-rational B-splines, the value of weights is null.
- evaluation
- A DANumber object that controls the spline evaluation.
Return Values
Returns the DAPoint3 object.
DAStatics Class
Point3SphericalAnimCreates a DAPoint3 object. The location of the point is given in spherical coordinates.
lib.Point3SphericalAnim(
XYangle,
YZangle,
length
)Parameters
- XYangle
- A DANumber object of the counter-clockwise 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
- A DANumber object of the counter-clockwise 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
- A DANumber object of the distance of the point from the origin. This must be an animated number.
Return Values
Returns the DAPoint3 object.
Remarks
The following table correlates Cartesian coordinates with polar coordinates (X means "Don't Care"):
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 [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
DAStatics Class
Point3SphericalSame as Point3SphericalAnim except that XYangle, YZangle, and length are non-animated numbers (doubles).
lib.Point3Spherical(
XYangle,
YZangle,
length
)DAStatics Class
SubPoint3Creates a DAVector3 object. The coordinate values of the vector are calculated by subtracting the coordinates of p3 from the corresponding coordinates of p1.
lib.SubPoint3(
p1,
p2
)Parameters
- p1 and p3
- The DAPoint3 objects.
Return Values
Returns the DAVector3 object.
DAStatics Class
SubPoint3VectorCreates 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.
lib.SubPoint3Vector(
pt,
vec
)Parameters
- pt
- A DAPoint3 object.
- vec
- A DAVector3 object.
Return Values
Returns the DAPoint3 object.
See Also
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