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> ## DAStatic Functions Relevant to DAVector3 Objects

> ###

> AddVector3

> DAStatics Class

> Creates a DAVector3 object. The direction and length of the vector are calculated by adding the corresponding coordinates of the given vectors.

> lib.AddVector3(
> v1,
> v2
> )

> ##### Parameters

> v1 and v2
>   The DAVector3 objects.

> ##### Return Values

> Returns the DAVector3 object.

> ##### See Also

> SubVector3

> ###

> CrossVector3

> DAStatics Class

> Creates a DAVector3 object that represents the "cross product" of the given vectors. The new vector has a length that is equal to the product of the lengths of the original vectors and the sine of the angle between them. The new vector has a direction that is perpendicular to the plane formed by the original vectors and that obeys the right-hand rule.

> lib.CrossVector3(
> v1,
> v2
> )

> ##### Parameters

> v1 and v2
>   The DAVector3 objects.

> ##### Return Values

> Returns the DAVector3 object.

> ###

> DerivativeVector3

> DAStatics Class

> Creates a DAVector3 object that is the instantaneous derivative (rate of change) of the given vector. For example, a constant vector behavior yields a constant derivative of [0 0 0], and Vector3(time, 0, 0) (without any additional time substitutions) yields a constant derivative vector of [1 0 0].

> lib.DerivativeVector3(
> vec
> )

> ##### Parameters

> vec
>   A DAVector3 object.

> ##### Return Values

> Returns the DAVector3 object.

> ###

> DotVector3

> DAStatics Class

> Creates DANumber object that represents the "dot product" of the given vectors. The dot product is the product of the lengths of the vectors and the cosine of the angle between them.

> lib.DotVector3(
> v1,
> v2
> )

> ##### Parameters

> v1 and v2
>   DAVector3 objects.

> ##### Return Values

> Returns the DANumber object.

> ###

> IntegralVector3

> DAStatics Class

> Creates a DAVector3 object that represents the sum of the all values of vec from the given start time to the present.

> lib.IntegralVector3(
> vec
> )

> ##### Parameters

> a
>   The DAVector3 object.

> ##### Return Values

> Returns the DAVector3 object.

> ###

> NegVector3

> DAStatics Class

> Creates a DAVector3 object that has the same length as the original vector, but points in the opposite direction.

> lib.NegVector3(
> v1
> )

> ##### Parameters

> v1
>   A DAVector3 object that is the original vector.

> ##### Return Values

> Returns the DAVector3 object.

> ###

> SubVector3

> DAStatics Class

> Creates a DAVector3 object. The direction and length of the vector are calculated by subtracting the coordinates of v2 from the corresponding coordinates of v1.

> lib.SubVector3(
> v1,
> v2
> )

> ##### Parameters

> v1 and v2
>   DAVector3 objects.

> ##### Return Values

> Returns the DAVector3 object.

> ##### See Also

> AddVector3

> ###

> Vector3Anim

> DAStatics Class

> Creates a DAVector3 object having a direction and length as specified by the given Cartesian coordinates.

> lib.Vector3Anim(
> x,
> y,
> z
> )

> ##### Parameters

> x, y, and z
>   The DANumber objects specifying the coordinate values. The x specifies a distance along the x-axis from the origin to a point, y specifies a distance along the y-axis, and z a distance along the z-axis. These must be animated numbers.

> ##### Return Values

> Returns the DAVector3 object.

> ##### See Also

> Vector3SphericalAnim

> ###

> Vector3

> DAStatics Class

> Same as Vector3Anim except that x, y, and z are non-animated numbers (doubles).

> lib.Vector3(
> x,
> y,
> z
> )

> ###

> Vector3BSpline

> DAStatics Class

> Creates a DAVector3 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 DAVector3 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.Vector3BSpline(
> 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 DAVector3 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 rational 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. This must be an animated number.

> ##### Return Values

> Returns the DAVector3 object.

> ###

> Vector3SphericalAnim

> DAStatics Class

> Creates a DAVector3 object having a direction and length as specified by the given spherical coordinates.

> lib.Vector3SphericalAnim(
> XYangle,
> YZangle,
> length
> )

> ##### Parameters

> XYangle
>   A DANumber object of the counter-clockwise XY angle, in radians, of the point about the positive y-axis. 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 specifying the length of the vector. This must be an animated number.

> ##### Return Values

> Returns the DAVector3 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

> Vector3Anim

> ###

> Vector3Spherical

> DAStatics Class

> Same as Vector3SphericalAnim except that XYangle, YZangle, and length are non-animated numbers (doubles).

> lib.Vector3Spherical(
> XYangle,
> YZangle,
> length
> )

> © 1998 Microsoft Corporation. All rights reserved. Terms of Use.

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