GLM_GTC_matrix_transform

Header: <glm/gtc/matrix_transform.hpp>

In this page, tmat4x4 stands for mat<4, 4, T, Q>, tvec3 stands for vec<3, T, Q> and tvec2 stands for vec<2, T, Q>.

Some notes on the convention

Coordinate system

Some functions use right handed coordinates by default. Define GLM_FORCE_LEFT_HANDED before including GLM to use left handed coordinate system by default.

Functions that are affected by this setting are:

• lookAt
• frustum, frustumNO, frustumZO
• ortho (for 3-dim), orthoNO, orthoZO
• perspective, perspectiveNO, perspectiveZO
• perspectiveFov, perspectiveFovNO, perspectiveFovZO
• infinitePerspective

Clip control

Some functions use the clip space \([-1,1]\) by default. Define GLM_FORCE_DEPTH_ZERO_TO_ONE to use \([0,1]\) clip space by default.

Functions that are affected by this setting are:

• frustum, frustumRH, frustumLH
• ortho (for 3-dim), orthoRH, orthoLH
• perspective, perspectiveRH, perspectiveLH
• perspectiveFov, perspectiveFovRH, perspectiveFovLH
• project
• unProject

Rotation, scaling, and translation

• rotate(tmat4x4 m, T angle, tvec3 axis) -> tmat4x4
• scale(tmat4x4 m, tvec3 v) -> tmat4x4
  • Returns \(m\cdot\begin{pmatrix} v_x & 0 & 0 & 0 \\ 0 & v_y & 0 & 0 \\ 0 & 0 & v_z & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
• translate(tmat4x4 m, tvec3 v) -> tmat4x4
  • Returns \(m\cdot\begin{pmatrix} 1 & 0 & 0 & v_x \\ 0 & 1 & 0 & v_y \\ 0 & 0 & 1 & v_z \\ 0 & 0 & 0 & 1 \end{pmatrix}\).

Viewing Transformation (from world coordinates to view coordinates)

• lookAt(tvec3 eye, tvec3 center, tvec3 up) -> tmat4x4
  • Alias for lookAtRH or lookAtLH.
  • Legacy OpenGL counterpart: gluLookAt
• lookAtRH(tvec3 eye, tvec3 center, tvec3 up) -> tmat4x4
  • Let \[\begin{aligned} f&:=\operatorname{normalize}(\mathrm{center}-\mathrm{eye}), \\ s&:=\operatorname{normalize}(f\times\mathrm{up}), \\ u&:=s\times f. \end{aligned}\]
  • Returns \(\begin{pmatrix} s_x & s_y & s_z & -s\cdot \mathrm{eye} \\ u_x & u_y & u_z & -u\cdot \mathrm{eye} \\ -f_x & -f_y & -f_z & f\cdot \mathrm{eye} \\ 0 & 0 & 0 & 1 \end{pmatrix}\), which is the matrix representation of the affine map \[\begin{array}{ccc} \mathbf{R}^3 & \to & \mathbf{R}^3 \\ v & \mapsto & \begin{pmatrix}s\cdot(v-\mathrm{eye})\\u\cdot(v-\mathrm{eye})\\-f\cdot(v-\mathrm{eye})\end{pmatrix}. \end{array}\]
• lookAtLH(tvec3 eye, tvec3 center, tvec3 up) -> tmat4x4
  • Let \[\begin{aligned} f&:=\operatorname{normalize}(\mathrm{center}-\mathrm{eye}), \\ s&:=\operatorname{normalize}(\mathrm{up}\times f), \\ u&:=f\times s. \end{aligned}\]
  • Returns \(\begin{pmatrix} s_x & s_y & s_z & -s\cdot \mathrm{eye} \\ u_x & u_y & u_z & -u\cdot \mathrm{eye} \\ f_x & f_y & f_z & f\cdot \mathrm{eye} \\ 0 & 0 & 0 & 1 \end{pmatrix}\), which is the matrix representation of the affine map \[\begin{array}{ccc} \mathbf{R}^3 & \to & \mathbf{R}^3 \\ v & \mapsto & \begin{pmatrix}s\cdot(v-\mathrm{eye})\\u\cdot(v-\mathrm{eye})\\f\cdot(v-\mathrm{eye})\end{pmatrix}. \end{array}\]

Projection (from view coordinates to clip coordinates)

• frustum(T left, T right, T bottom, T top, T near, T far) -> mat<4, 4, T, defaultp>
  • Alias for frustumRH_NO, frustumRH_ZO, frustumLH_NO, or frustumLH_ZO.
  • Legacy OpenGL counterpart: glFrustum
• frustumRH: Alias for frustumRH_NO or frustumRH_ZO.
• frustumLH: Alias for frustumLH_NO or frustumLH_ZO.
• frustumNO: Alias for frustumRH_NO or frustumLH_NO.
• frustumZO: Alias for frustumRH_ZO or frustumLH_ZO.
• frustumRH_NO(T left, T right, T bottom, T top, T near, T far) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2\mathrm{near}}{\mathrm{right}-\mathrm{left}} & 0 & \frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} & 0 \\ 0 & \frac{2\mathrm{near}}{\mathrm{top}-\mathrm{bottom}} & \frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} & 0 \\ 0 & 0 & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} & -\frac{2\mathrm{far}\cdot\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & -1 & 0 \end{pmatrix}\).
• frustumRH_ZO(T left, T right, T bottom, T top, T near, T far) -> mat<4, 4, T, defaultp>
• frustumLH_NO(T left, T right, T bottom, T top, T near, T far) -> mat<4, 4, T, defaultp>

• frustumLH_ZO(T left, T right, T bottom, T top, T near, T far) -> mat<4, 4, T, defaultp>

• ortho(T left, T right, T bottom, T top) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2}{\mathrm{right}-\mathrm{left}} & 0 & 0 & -\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} \\ 0 & \frac{2}{\mathrm{top}-\mathrm{bottom}} & 0 & -\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
  • Legacy OpenGL counterpart: gluOrtho2D
• ortho(T left, T right, T bottom, T top, T zNear, T zFar) -> mat<4, 4, T, defaultp>
  • Alias for orthoRH_NO, orthoRH_ZO, orthoLH_NO, or orthoLH_ZO.
  • Legacy OpenGL counterpart: glOrtho
• orthoRH: Alias for orthoRH_NO or orthoRH_ZO.
• orthoLH: Alias for orthoLH_NO or orthoLH_ZO.
• orthoNO: Alias for orthoRH_NO or orthoLH_NO.
• orthoZO: Alias for orthoRH_NO or orthoLH_NO.
• orthoLH_NO(T left, T right, T bottom, T top, T zNear, T zFar) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2}{\mathrm{right}-\mathrm{left}} & 0 & 0 & -\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} \\ 0 & \frac{2}{\mathrm{top}-\mathrm{bottom}} & 0 & -\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} \\ 0 & 0 & \frac{2}{\mathrm{far}-\mathrm{near}} & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
• orthoLH_ZO(T left, T right, T bottom, T top, T zNear, T zFar) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2}{\mathrm{right}-\mathrm{left}} & 0 & 0 & -\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} \\ 0 & \frac{2}{\mathrm{top}-\mathrm{bottom}} & 0 & -\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} \\ 0 & 0 & \frac{1}{\mathrm{far}-\mathrm{near}} & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
• orthoRH_NO(T left, T right, T bottom, T top, T zNear, T zFar) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2}{\mathrm{right}-\mathrm{left}} & 0 & 0 & -\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} \\ 0 & \frac{2}{\mathrm{top}-\mathrm{bottom}} & 0 & -\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} \\ 0 & 0 & -\frac{2}{\mathrm{far}-\mathrm{near}} & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
• orthoRH_ZO(T left, T right, T bottom, T top, T zNear, T zFar) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{2}{\mathrm{right}-\mathrm{left}} & 0 & 0 & -\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}} \\ 0 & \frac{2}{\mathrm{top}-\mathrm{bottom}} & 0 & -\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}} \\ 0 & 0 & -\frac{1}{\mathrm{far}-\mathrm{near}} & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & 0 & 1 \end{pmatrix}\).
• perspective(T fovy, T aspect, T near, T far) -> mat<4, 4, T, defaultp>
  • Alias for perspectiveRH_NO, perspectiveRH_ZO, perspectiveLH_NO or perspectiveLH_ZO.
  • Legacy OpenGL counterpart: gluPerspective
• perspectiveRH: Alias for perspectiveRH_NO or perspectiveRH_ZO.
• perspectiveLH: Alias for perspectiveLH_NO or perspectiveLH_ZO.
• perspectiveNO: Alias for perspectiveRH_NO or perspectiveLH_NO.
• perspectiveZO: Alias for perspectiveRH_ZO or perspectiveLH_ZO.
• perspectiveRH_NO(T fovy, T aspect, T near, T far) -> mat<4, 4, T, defaultp>
  • Returns \(\begin{pmatrix} \frac{1}{\mathrm{aspect}\cdot\tan(\mathrm{fovy}/2)} & 0 & 0 & 0 \\ 0 & \frac{1}{\tan(\mathrm{fovy}/2)} & 0 & 0 \\ 0 & 0 & -\frac{\mathrm{far}+\mathrm{near}}{\mathrm{far}-\mathrm{near}} & -\frac{2\mathrm{far}\cdot\mathrm{near}}{\mathrm{far}-\mathrm{near}} \\ 0 & 0 & -1 & 0 \end{pmatrix}\).
• perspectiveRH_ZO(T fovy, T aspect, T near, T far) -> mat<4, 4, T, defaultp>
• perspectiveLH_NO(T fovy, T aspect, T near, T far) -> mat<4, 4, T, defaultp>

• perspectiveLH_ZO(T fovy, T aspect, T near, T far) -> mat<4, 4, T, defaultp>

• perspectiveFov(T fovy, T width, T height, T near, T far) -> mat<4, 4, T, defaultp>
  • Alias for perspectiveFovRH_NO, perspectiveFovRH_ZO, perspectiveFovLH_NO or perspectiveFovLH_ZO.
• perspectiveFovRH: Alias for perspectiveFovRH_NO or perspectiveFovRH_ZO.
• perspectiveFovLH: Alias for perspectiveFovLH_NO or perspectiveFovLH_ZO.
• perspectiveFovNO: Alias for perspectiveFovRH_NO or perspectiveFovLH_NO.
• perspectiveFovZO: Alias for perspectiveFovRH_ZO or perspectiveFovLH_ZO.
• perspectiveFovRH_NO(T fovy, T width, T height, T near, T far) -> mat<4, 4, T, defaultp>
• perspectiveFovRH_ZO(T fovy, T width, T height, T near, T far) -> mat<4, 4, T, defaultp>
• perspectiveFovLH_NO(T fovy, T width, T height, T near, T far) -> mat<4, 4, T, defaultp>

• perspectiveFovLH_ZO(T fovy, T width, T height, T near, T far) -> mat<4, 4, T, defaultp>

• infinitePerspective(T fovy, T aspect, T near) -> mat<4, 4, T, defaultp>
  • Alias for infinitePerspectiveRH or infinitePerspectiveLH.
• infinitePerspectiveRH(T fovy, T aspect, T near) -> mat<4, 4, T, defaultp>

• infinitePerspectiveLH(T fovy, T aspect, T near) -> mat<4, 4, T, defaultp>

???

• pickMatrix(tvec2 center, tvec2 delta, vec<4, U, Q> viewport) -> tmat4x4
• project(tvec3 obj, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3
  • Alias for projectNO or projectZO.
• projectNO(tvec3 obj, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3
• projectZO(tvec3 obj, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3
• tweakedInfinitePerspective(T fovy, T aspect, T near) -> mat<4, 4, T, defaultp>
• tweakedInfinitePerspective(T fovy, T aspect, T near, T ep) -> mat<4, 4, T, defaultp>
• unProject(tvec3 win, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3
  • Alias for unProjectNO or unprojectZO.
• unProjectNO(tvec3 win, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3
• unProjectZO(tvec3 win, tmat4x4 model, tmat4x4 proj, vec<4, U, Q> viewport) -> tvec3

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