## DAStatic Functions Relevant to DAPoint3 Objects

###

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.

lib.AddPoint3Vector(
pt,
vec
)

##### Parameters

pt
  A DAPoint3 object.
vec
  A DAVector3 object.

##### Return Values

Returns the DAPoint3 object.

##### See Also

SubPoint3Vector

###

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].

lib.DerivativePoint3(
pt
)

##### Parameters

pt
  A DAPoint3 object.

##### Return Values

Returns the DAVector3 object.

###

DistancePoint3

DAStatics Class

Creates 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

DistanceSquaredPoint3

###

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.

lib.DistanceSquaredPoint3(
p1,
p2
)

##### Parameters

p1 and p3
  The DAPoint3 objects.

##### Return Values

Returns the DANumber object.

##### See Also

DistancePoint3

###

Point3Anim

DAStatics Class

Creates 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

Point3SphericalAnim

###

Point3

DAStatics Class

Same as Point3Anim except that x, y, and z are non-animated numbers (doubles).

lib.Point3(
x,
y,
z
)

###

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).

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.

###

Point3SphericalAnim

DAStatics Class

Creates 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

Point3Anim

###

Point3Spherical

DAStatics Class

Same as Point3SphericalAnim except that XYangle, YZangle, and length are non-animated numbers (doubles).

lib.Point3Spherical(
XYangle,
YZangle,
length
)

###

SubPoint3

DAStatics Class

Creates 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.

###

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.

lib.SubPoint3Vector(
pt,
vec
)

##### Parameters

pt
  A DAPoint3 object.
vec
  A DAVector3 object.

##### Return Values

Returns the DAPoint3 object.

##### See Also

AddPoint3Vector

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