DAStatics Functions Relevant to DAVector2 Objects

AddVector2 Creates a DAVector2 object that is the vector-valued sum of the two vectors.

DerivativeVector2 Creates a DAVector2 object that is the instantaneous derivative (rate of change) of the given vector.

DotVector2 Creates a DANumber object that represents the "dot product" of the given vectors.

IntegralVector2 Creates a DAVector2 object that represents the sum of all the values of vec from the given start time to the present.

NegVector2 Creates a DAVector2 object that is the same length as the original vector but points in the opposite direction.

SubVector2 Creates a DAVector2 object. The direction and length of the vector are calculated by subtracting the coordinates of v2 from the corresponding coordinates of v1.

Vector2 Creates a DAVector2 object having a direction and length as specified by the given Cartesian coordinates. Same as Vector2Anim except that x and y are nonanimated numbers (doubles).

Vector2Anim Creates a DAVector2 object having a direction and length as specified by the given Cartesian coordinates.

Vector2BSpline Creates a DAVector2 object based on a B-spline function.

Vector2Polar Creates a DAVector2 object having a direction and length as specified by the given polar coordinates. Same as Vector2PolarAnim except that XYangle and length are nonanimated numbers (doubles).

Vector2PolarAnim Creates a DAVector2 object having a direction and length as specified by the given polar coordinates.

Vector2PolarDegrees Creates a DAVector2 object having a direction and length as specified by the given polar coordinates.

AddVector2

DAStatics Class

Creates a DAVector2 object that is the vector-valued sum of the two vectors.

Syntax

lib.AddVector2( v1, v2 )

Parameters

v1 and v2
DAVector2 objects to be added.

Return Value

Returns the DAVector2 object.

See Also

SubVector2

DerivativeVector2

DAStatics Class

Creates a DAVector2 object that is the instantaneous derivative (rate of change) of the given vector. For example, a constant vector yields a constant derivative of [0 0], and Vector2 (time, 0) (without any additional time substitutions) yields a constant derivative vector of [1 0].

Syntax

lib.DerivativeVector2( vec )

Parameters

vec
DAVector2 object.

Return Value

Returns the DAVector2 object.

DotVector2

DAStatics Class

Creates a DANumber object that represent 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.

Syntax

lib.DotVector2( v1, v2 )

Parameters

v1 and v2
DAVector2 objects.

Return Value

Returns the DANumber object.

IntegralVector2

DAStatics Class

Creates a DAVector2 object that represents the sum of all the values of vec from the given start time to the present.

Syntax

lib.IntegralVector2( vec )

Parameters

vec
DAVector2 object.

Return Value

Returns the DAVector2 object.

NegVector2

DAStatics Class

Creates a DAVector2 object that is the same length as the original vector but points in the opposite direction.

Syntax

lib.NegVector2( v1 )

Parameters

v1
DAVector2 object that is the original vector.

Return Value

Returns the DAVector2 object.

SubVector2

DAStatics Class

Creates a DAVector2 object. The direction and length of the vector are calculated by subtracting the coordinates of v2 from the corresponding coordinates of v1.

Syntax

lib.SubVector2( v1, v2 )

Parameters

v1 and v2
DAVector2 objects.

Return Value

Returns the DAVector2 object.

See Also

AddVector2

Vector2

DAStatics Class

Creates a DAVector2 object having a direction and length as specified by the given Cartesian coordinates. Same as Vector2Anim except that x and y are nonanimated numbers (doubles).

Syntax

lib.Vector2( x, y )

Parameters

x
A double value specifying the distance along the x-axis from the origin to a point. This is a nonanimated number.
y
A double value specifying the distance along the y-axis. This is a nonanimated number.

Return Value

Returns the DAVector2 object.

Vector2Anim

DAStatics Class

Creates a DAVector2 object having a direction and length as specified by the given Cartesian coordinates.

Syntax

lib.Vector2Anim( x, y )

Parameters

x
DANumber object specifying the distance along the x-axis from the origin to a point. This must be an animated number.
y
DANumber object specifying the distance along the y-axis. This must be an animated number.

Return Value

Returns the DAVector2 object.

See Also

Vector2Polar

Vector2BSpline

DAStatics Class

Creates a DAVector2 object 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.Vector2BSpline( degree, knots, control_elements, weights, evaluation )

Parameters

degree
Number (a 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 DAVector2 objects representing the control elements used to calculate the B-spline.
weights
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 nonrational B-splines, the value of weights is null.
evaluation
DANumber object that controls the spline evaluation. This must be an animated number.

Return Value

Returns the DAVector2 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 DAVector2 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.

Vector2Polar

DAStatics Class

Creates a DAVector2 object having a direction and length as specified by the given polar coordinates. Same as Vector2PolarAnim except that XYangle and length are nonanimated numbers (doubles).

Syntax

lib.Vector2Polar( XYangle, length )

Parameters

XYangle
A double value that is the counterclockwise angle of the vector, in radians, from the positive x-ray. This is a nonanimated number.
length
A double value that is the length of the vector. This is a nonanimated number.

Return Value

Returns the DAVector2 object.

Vector2PolarAnim

DAStatics Class

Creates a DAVector2 object having a direction and length as specified by the given polar coordinates.

Syntax

lib.Vector2PolarAnim( XYangle, length )

Parameters

XYangle
DANumber object that is the counter-clockwise angle of the vector, in radians, from the positive x-ray. This must be an animated number.
length
DANumber object that is the length of the vector. This must be an animated number.

Return Value

Returns the DAVector2 object.

See Also

Vector2Anim

Vector2PolarDegrees

DAStatics Class

Creates a DAVector2 object having a direction and length as specified by the given polar coordinates.

Syntax

lib.Vector2PolarDegrees( XYangle, length )

Parameters

XYangle
Number (a double) that is the counter-clockwise angle of the vector (expressed in degrees) from the positive x-ray.
length
Number (a double) that is the length of the vector.

Return Value

Returns the DAVector2 object.