Gives the matrix that changes nothing, as a starting point or a placeholder.
Example: [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
The identity matrix
Builds a rotation about an axis that passes through a center point.
The result is three matrices applied in order: move the center to the origin, rotate, move back. The angle is in degrees; positive turns counter-clockwise when the axis points toward you. Example: center [5,0,0], axis [0,1,0], angle 90 -> a quarter turn about the vertical line through [5,0,0]
The axis direction, the center it passes through and the angle in degrees
The list of matrices to apply in order
Builds a rotation about a line parallel to the X axis through a center point.
The result is three matrices applied in order: move the center to the origin, rotate, move back. The angle is in degrees; positive turns counter-clockwise when the axis points toward you. Example: center [0,0,0], angle 90 -> a quarter turn about the X axis
The center and the angle in degrees
The list of matrices to apply in order
Builds a rotation about a line parallel to the Y axis through a center point.
The result is three matrices applied in order: move the center to the origin, rotate, move back. The angle is in degrees; positive turns counter-clockwise when the axis points toward you. Example: center [0,0,0], angle 90 -> a quarter turn about the Y axis
The center and the angle in degrees
The list of matrices to apply in order
Builds a rotation about a line parallel to the Z axis through a center point.
The result is three matrices applied in order: move the center to the origin, rotate, move back. The angle is in degrees; positive turns counter-clockwise when the axis points toward you. Example: center [0,0,0], angle 90 -> a quarter turn about the Z axis
The center and the angle in degrees
The list of matrices to apply in order
Builds a rotation from three angles about a center point: yaw turns about Y, pitch about X and roll about Z.
The result is three matrices applied in order: move the center to the origin, rotate, move back. Angles are in degrees. Example: yaw 90, pitch 0, roll 0 -> a quarter turn about the vertical axis
The yaw, pitch and roll in degrees and the center
The list of matrices to apply in order
Builds a scale with its own factor per axis, measured from a center point that stays in place.
The result is three matrices applied in order: move the center to the origin, scale, move back. Example: center [5,5,5], factors [2,1,0.5] -> doubles X, keeps Y, halves Z about [5,5,5]
The center and the factor for each axis
The list of matrices to apply in order
Builds a scale with its own factor per axis, measured from the origin.
Example: factors [2,3,1] -> doubles X, triples Y, keeps Z
The factor for each axis
A list with the one scale matrix
Builds a stretch along one direction, measured from a center point; distances across that direction stay as they are.
The result is three matrices applied in order: move the center to the origin, stretch, move back. Example: center [0,0,0], direction [1,0,0], scale 2 -> everything twice as far from the center along X
The center, the direction and the factor
The list of matrices to apply in order
Builds a scale by the same factor on every axis, measured from the origin.
Example: 2 -> everything twice as big and twice as far from the origin
The factor
A list with the one scale matrix
Builds a scale by the same factor on every axis, measured from a center point that stays in place.
The result is three matrices applied in order: move the center to the origin, scale, move back. Example: center [5,5,5], scale 0.5 -> everything half as big, shrinking toward [5,5,5]
The factor and the center
The list of matrices to apply in order
Builds a move by a vector.
Example: [10,5,0] -> 10 along X, 5 along Y, nothing along Z
The vector to move by
A list with the one translation matrix
Builds one move per vector, for transforming many points each by its own vector.
Example: [[1,0,0], [0,2,0]] -> two transformations: one along X, one along Y
The vectors to move by
One transformation per vector, in the same order
Builds transformation matrices for moving, rotating, scaling and stretching geometry. A transformation is a 4x4 matrix as 16 numbers in column-major order; most methods return a short list of them that is applied in order, so a rotation about a point is a move to the origin, the rotation, and the move back. Angles are in degrees. Apply the result with the transform methods of
point,polyline,lineand the kernels.