affine_rts

Similarity transform: rotation + translation + uniform scaling.

module 09_geometric_transformationsource: affine_rts.hpp

3 functions take it 0 return it 24 operators

T * p scales, rotates and then translates: affine_rt gives R p + t, affine_rts gives R s p + t, and affine gives R s S p + t, where S = diag(scaling_xyz) stretches the local axes of the shape before the rotation. Tap to enlarge.

Fields and methods

Members of the struct affine_rts. Most of what you do with a CGP type goes through the free functions listed below.

Fields

`rotation_transform rotation`	Rotation part of the similarity transform.
`vec3 translation`	Translation part of the similarity transform, applied after the scaling and the rotation.
`float scaling`	Uniform scaling factor, applied before the rotation (default 1).

Methods

`affine_rts()`	Builds the identity transform (identity rotation, zero translation, scaling 1).3 overloads src
`affine_rts(affine_rt const& T)`	Builds the similarity with the rotation and translation of a rigid transform and scaling 1 (implicit conversion). src
`affine_rts(rotation_transform const& rotation, vec3 const& translation, float scaling)`	Builds the similarity p -> scaling(rotationp) + translation (explicit). src
`affine_rts& set_scaling(float scaling)`	Sets the uniform scaling factor and returns a reference to the transform. src
`affine_rts& set_translation(vec3 const& translation)`	Sets the translation and returns a reference to the transform. src
`affine_rts& set_rotation(rotation_transform const& rotation)`	Sets the rotation and returns a reference to the transform. src
`mat4 matrix() const`	Returns the 4x4 matrix ((s R, t), (0, 1)) of the transform. src

Functions taking a affine_rts

Transform 1

inverse

source

affine_rts inverse(affine_rts const& T)

Inverse affine transform.

Convert 2

str

source

std::string str(affine_rts const& T)

String listing the rotation (quaternion), translation and scaling of the transform.

type_str

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std::string type_str(affine_rts const&)

Type name "affine_rts".

Functions returning a affine_rts

None.

Operators

Show the 24 operators (+, -, *, ==, ...)

operator*

10 overloads

affine operator*(affine_rts const& T1, affine const& T2)

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Composition T1 o T2 of a rotation-translation-scaling (parent) with an affine transform (child), exact for any scaling_xyz.

vec3 operator*(affine_rts const& T, vec3 const& p)

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Apply the transform to a point: scaling * (rotation * p) + translation.

vec4 operator*(affine_rts const& T, vec4 const& p)

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Apply the transform to a homogeneous vector, the translation being weighted by w.

affine_rts operator*(affine_rts const& T1, affine_rts const& T2)

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Composition T1 o T2 of two rotation-translation-scaling transforms.

affine_rts operator*(affine_rts const& T, rotation_transform const& R)

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Transform T o R: the rotation is applied before T.

affine_rts operator*(float s, affine_rts const& T)

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Copy of the transform with its scaling multiplied by s, the translation being left unchanged.

affine_rts operator*(affine_rts const& T, float s)

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Copy of the transform with its scaling multiplied by s, the translation being left unchanged.

affine_rts operator*(affine_rts const& T1, affine_rt const& T2)

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Composition T1 o T2 of a rotation-translation-scaling with a rigid transform.

mat4 operator*(affine_rts const& T1, mat4 const& T2)

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Product of the 4x4 matrix of the transform with a mat4.

mat4 operator*(affine_rts const& T1, mat3 const& T2)

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Product of the 4x4 matrix of the transform with a mat3 extended to a mat4.

operator+

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affine_rts operator+(affine_rts const& T, vec3 const& tr)

Copy of the transform with tr added to its translation.

operator-

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affine_rts operator-(affine_rts const& T, vec3 const& tr)

Copy of the transform with tr subtracted from its translation.

operator/

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affine_rts operator/(affine_rts const& T, float s)

Copy of the transform with its scaling divided by s, the translation being left unchanged.

operator<<

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std::ostream& operator<<(std::ostream& s, affine_rts const& T)

Write str(T) of the transform to the stream.

Documented on another page

operator*Composition T1 o T2 of an affine transform with a rotation-translation-scaling, returned as an affine; asserts that T1.scaling_xyz is uniform (use T1.matrix()*T2.matrix() otherwise).on affine
operator*x33 overloadson rotation_transform
operator*x33 overloadson affine_rt
operator*Product of a mat4 with the 4x4 matrix of the transform.on mat4
operator*Product of a mat3 extended to a mat4 with the 4x4 matrix of the transform.on mat3
operator+Copy of the transform with tr added to its translation.on vec3