IC Python API:Transform Math

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Revision as of 23:36, 17 February 2020 by Chuck (RL) (Talk | contribs) (Transform Point)

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This article will go some recipes for common 3D transformational math. You'll find this helpful if you need to perform spacial calculations.

Transform Point

Transforms position of a point from local-space to world-space. The returned position is affected by scale.

def transform_point(world_transform, local_position):
    # Get the transform matrix4
    world_matrix = world_transform.Matrix()

    # New matrix4 for the local position
    point_world_matrix = RLPy.RMatrix4()
    point_world_matrix.MakeIdentity()
    point_world_matrix.SetTranslate(local_position)

    # Combine the 2 matrix4s
    point_world_matrix = point_world_matrix * world_matrix

    # Return the translation element of the combined matrix4
    return RLPy.RVector3(point_world_matrix.GetTranslate())

In order to specify the rotation in world-space, use the following instead:

def transform_point(world_transform, specific_rotation, local_position):
    # Get the transform matrix4
    world_matrix = world_transform.Matrix()
    world_matrix.SetSR(specific_rotation)

    # New matrix4 for the local position
    point_world_matrix = RLPy.RMatrix4()
    point_world_matrix.MakeIdentity()
    point_world_matrix.SetTranslate(local_position)

    # Combine the 2 matrix4
    point_world_matrix = point_world_matrix * world_matrix

    # Return the translation element of the combined matrix4
    return RLPy.RVector3(point_world_matrix.GetTranslate())

Inverse Transform Point

Transforms a position point from world-space to local-space. This function is the opposite of Transform Point, which is used to convert local to world-space.

def inverse_transform_point(world_transform, world_point):
    transform_matrix = world_transform.Matrix()
    local_position = world_point - transform_matrix.GetTranslate()  # Can also use transform.T()
    transform_matrix.SetTranslate(RLPy.RVector3.ZERO)  # Zero out transform matrix translation

    # New matrix4 for the local position
    point_world_matrix = RLPy.RMatrix4()
    point_world_matrix.MakeIdentity()
    point_world_matrix.SetTranslate(local_position)

    # Convert local space to transform space
    point_transform_matrix = point_world_matrix * transform_matrix.Inverse()

    # Return the translation element of the combined matrix4
    return point_transform_matrix.GetTranslate()

Transform Direction

Transforms direction of a vector from local-space to world-space. The returned vector has the same length as the direction.

def transform_direction(world_transform, local_position):
    # Get the transform rotation 3x3 matrix
    world_rot_matrix = world_transform.Rotate()

    # New matrix4 for world direction
    world_dir = RLPy.RMatrix4()
    world_dir.MakeIdentity()
    world_dir.SetSR(world_rot_matrix)

    # New matrix for the local position
    point_world_matrix = RLPy.RMatrix4()
    point_world_matrix.MakeIdentity()
    point_world_matrix.SetTranslate(local_position)

    # Combine the 2 matrix4
    point_world_matrix = point_world_matrix * world_dir

    # Return the translation element of the combined matrix4
    return RLPy.RVector3(point_world_matrix.GetTranslate())