Transform¶

template<IsFloatingPoint T> struct Transform¶

Rigid body transform with position, rotation, scale, and kinematic quantities.

Represents a 3D transformation including translation, rotation, scale, velocity, and angular velocity. Provides methods for conversion to matrix, inversion, composition, and application to points, directions, and velocities.

Template Parameters:: T – Floating point type (float or double)

Public Functions

template<IsFloatingPoint U> explicit operator Transform<U>() const¶

Convert this Transform to another floating point type.

Template Parameters:: U – Target floating point type
Returns:: Transform

Mat4<T> to_matrix() const¶

Convert the transform to a 4x4 matrix (T * R * S).

Returns:: Mat4<T> Transformation matrix

Transform<T> inverse() const¶

Compute the inverse of the transform.

Returns:: Transform<T> Inverse transform

Transform<T> operator*(const Transform<T> &b) const¶

Compose this transform with another.

Parameters:: b – Other transform
Returns:: Transform<T> Composed transform

Vec3<T> apply_to_point(const Vec3<T> &point) const¶

Apply the transform to a point (scale, rotate, translate).

Parameters:: point – Point to transform
Returns:: Vec3<T> Transformed point

Vec3<T> apply_to_direction(const Vec3<T> &dir) const¶

Apply the transform to a direction (scale, rotate).

Parameters:: dir – Direction to transform
Returns:: Vec3<T> Transformed direction

Vec3<T> apply_to_velocity(const Vec3<T> &vel) const¶

Apply the transform to a velocity (scale, rotate, add velocity).

Parameters:: vel – Velocity to transform
Returns:: Vec3<T> Transformed velocity

Vec3<T> apply_to_angular_velocity(const Vec3<T> &ang_vel) const¶

Apply the transform to an angular velocity (rotate, add angular velocity).

Parameters:: ang_vel – Angular velocity to transform
Returns:: Vec3<T> Transformed angular velocity

Vec3<T> velocity_of_point(const Vec3<T> &point) const¶

Compute the velocity of a point in this reference frame.

Compute the velocity of a point rigidly attached to this frame.

Parameters:: point – Point in world coordinates
Returns:: Vec3<T> Velocity of the point

Vec3<T> velocity_of_local_point(const Vec3<T> &local_point) const¶

Compute the velocity of a point expressed in local coordinates.

Compute the velocity of a point specified in local coordinates.

Parameters:: local_point – Point in local coordinates
Returns:: Vec3<T> Velocity of the point

Public Members

Vec3<T> position = {0, 0, 0}¶

Rotation<T> rotation = {}¶

Vec3<T> scale = {1, 1, 1}¶

Vec3<T> velocity = {0, 0, 0}¶

Vec3<T> angular_velocity = {0, 0, 0}¶