A namespace for 3D transformation factory functions. More...

#include <transform.hpp>

Public Member Functions
constexpr	Transform (const Mat4 &mat)
constexpr const Mat4 &	mat () const
constexpr Transform &	*operator=** (const Transform &rhs) noexcept
constexpr Transform	operator* (const Transform &rhs) const noexcept
constexpr Pt3	operator* (const Pt3 &point) const noexcept
	Transforms a point using the transform matrix.
constexpr Vec3	operator* (const Vec3 &vec) const noexcept
	Transforms a vector using the transform matrix.
constexpr Normal3	operator* (const Normal3 &normal) const noexcept
	Transforms a normal using the transform matrix.
constexpr Ray3	operator* (const Ray3 &ray) const noexcept
constexpr Bound3	operator* (const Bound3 &bound) const noexcept

Static Public Member Functions
static constexpr Transform	translate (const Vec3 &t) noexcept
	Creates a 4x4 translation matrix.
static constexpr Transform	scale (Float s) noexcept
	Creates a 4x4 uniform scaling matrix.
static constexpr Transform	scale (const Vec3 &s) noexcept
	Creates a 4x4 non-uniform scaling matrix.
static constexpr Transform	rotate_x (Float angle_rad) noexcept
	Creates a 4x4 rotation matrix around the X-axis.
static constexpr Transform	rotate_y (Float angle_rad) noexcept
	Creates a 4x4 rotation matrix around the Y-axis.
static constexpr Transform	rotate_z (Float angle_rad) noexcept
	Creates a 4x4 rotation matrix around the Z-axis.
static constexpr Transform	rotate (Float angle_rad, const Vec3 &axis) noexcept
	Creates a rotation matrix from an arbitrary axis and an angle (Rodrigues' rotation formula).
static constexpr Transform	look_at (const Pt3 &eye, const Pt3 &target, const Vec3 &up) noexcept
	Creates a view matrix (a.k.a. camera matrix) using the "look-at" method.
static constexpr Transform	perspective (Float fov_y_rad, Float aspect_ratio, Float z_near, Float z_far) noexcept
	Creates a left-handed perspective projection matrix.
static constexpr Transform	orthographic (Float left, Float right, Float bottom, Float top, Float z_near, Float z_far) noexcept
	Creates a left-handed orthographic projection matrix.

Detailed Description

A namespace for 3D transformation factory functions.

This namespace contains static functions to generate common 3D transformation matrices. Each function corresponds to a specific transformation (translation, rotation, scaling, etc.) and returns a Mat4 (4x4 matrix) that can be used in 3D rendering or other applications.

Member Function Documentation

◆ look_at()

constexpr Transform pbpt::math::Transform::look_at	(	const Pt3 &	eye,
		const Pt3 &	target,
		const Vec3 &	up )

inlinestaticconstexprnoexcept

Creates a view matrix (a.k.a. camera matrix) using the "look-at" method.

This matrix transforms coordinates from world space to view (camera) space.

Parameters

eye	The position of the camera in world space.
target	The point in world space that the camera is looking at.
up	A vector indicating the "up" direction of the world (usually (0, 1, 0)).

Returns: A Mat4 representing the view transformation.

◆ operator*() [1/3]

Normal3 pbpt::math::Transform::operator* ( const Normal3 & normal ) const

inlineconstexprnoexcept

Transforms a normal using the transform matrix.

Parameters

normal The normal to transform.

Returns: The transformed normal.

◆ operator*() [2/3]

Pt3 pbpt::math::Transform::operator* ( const Pt3 & point ) const

inlineconstexprnoexcept

Transforms a point using the transform matrix.

Parameters

point The point to transform.

Returns: The transformed point.

◆ operator*() [3/3]

Vec3 pbpt::math::Transform::operator* ( const Vec3 & vec ) const

inlineconstexprnoexcept

Transforms a vector using the transform matrix.

Parameters

vec	The vector to transform.

Returns: The transformed vector.

◆ orthographic()

constexpr Transform pbpt::math::Transform::orthographic	(	Float	left,
		Float	right,
		Float	bottom,
		Float	top,
		Float	z_near,
		Float	z_far )

inlinestaticconstexprnoexcept

Creates a left-handed orthographic projection matrix.

This matrix transforms coordinates from view space to clip space without any perspective distortion. It maps a rectangular box (view volume) to the canonical view volume [-1, 1]^3.

Parameters

left	The x-coordinate of the left clipping plane.
right	The x-coordinate of the right clipping plane.
bottom	The y-coordinate of the bottom clipping plane.
top	The y-coordinate of the top clipping plane.
z_near	The z-coordinate of the near clipping plane.
z_far	The z-coordinate of the far clipping plane.

Returns: A Mat4 representing the orthographic projection.

◆ perspective()

constexpr Transform pbpt::math::Transform::perspective	(	Float	fov_y_rad,
		Float	aspect_ratio,
		Float	z_near,
		Float	z_far )

inlinestaticconstexprnoexcept

Creates a left-handed perspective projection matrix.

This matrix transforms coordinates from view space to clip space, creating the illusion of depth.

Parameters

fov_y_rad	Vertical field of view, in radians.
aspect_ratio	The aspect ratio of the viewport (width / height).
z_near	Distance to the near clipping plane (must be positive).
z_far	Distance to the far clipping plane (must be positive and > z_near).

Returns: A Mat4 representing the perspective projection.

◆ rotate()

constexpr Transform pbpt::math::Transform::rotate	(	Float	angle_rad,
		const Vec3 &	axis )

inlinestaticconstexprnoexcept

Creates a rotation matrix from an arbitrary axis and an angle (Rodrigues' rotation formula).

Parameters

angle_rad	The rotation angle in radians.
axis	The axis of rotation. Should be a unit vector for correct results.

Returns: A Mat4 that performs the specified rotation.

◆ rotate_x()

constexpr Transform pbpt::math::Transform::rotate_x ( Float angle_rad )

inlinestaticconstexprnoexcept

Creates a 4x4 rotation matrix around the X-axis.

Parameters

angle_rad The rotation angle in radians.

Returns: A Mat4 that rotates points/vectors around the world's X-axis.

◆ rotate_y()

constexpr Transform pbpt::math::Transform::rotate_y ( Float angle_rad )

inlinestaticconstexprnoexcept

Creates a 4x4 rotation matrix around the Y-axis.

Parameters

angle_rad The rotation angle in radians.

Returns: A Mat4 that rotates points/vectors around the world's Y-axis.

◆ rotate_z()

constexpr Transform pbpt::math::Transform::rotate_z ( Float angle_rad )

inlinestaticconstexprnoexcept

Creates a 4x4 rotation matrix around the Z-axis.

Parameters

angle_rad The rotation angle in radians.

Returns: A Mat4 that rotates points/vectors around the world's Z-axis.

◆ scale() [1/2]

constexpr Transform pbpt::math::Transform::scale ( const Vec3 & s )

inlinestaticconstexprnoexcept

Creates a 4x4 non-uniform scaling matrix.

Parameters

s	A Vec3 containing the scaling factors for the x, y, and z axes.

Returns: A Mat4 that scales a point or vector non-uniformly.

◆ scale() [2/2]

constexpr Transform pbpt::math::Transform::scale ( Float s )

inlinestaticconstexprnoexcept

Creates a 4x4 uniform scaling matrix.

Parameters

s	The scalar factor to scale by on all axes.

Returns: A Mat4 that scales a point or vector uniformly.

◆ translate()

constexpr Transform pbpt::math::Transform::translate ( const Vec3 & t )

inlinestaticconstexprnoexcept

Creates a 4x4 translation matrix.

Parameters

t	A Vec3 representing the translation amounts (tx, ty, tz).

Returns: A Mat4 that translates a point by the given vector.

The documentation for this class was generated from the following file:

/Users/jinceyang/Desktop/codebase/pbpt/engine/math/transform.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ look_at()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ orthographic()

◆ perspective()

◆ rotate()

◆ rotate_x()

◆ rotate_y()

◆ rotate_z()

◆ scale() [1/2]

◆ scale() [2/2]

◆ translate()