Math Matrix Functions

Math Class

Members

mat4 cubeTransform ( int face ) #

Arguments

• int face - Cube face number.

Return value

mat4 frustum ( float left, float right, float bottom, float top, float znear, float zfar ) #

Coordinates of top, left, right, bottom are set relatively to center point of the znear plane.

There are two different points (A and B) on the picture above. Since the top, left, right, bottom are coordinates relatively to the center point of the znear plane, coordinates of the A point should be A(left, bottom, znear). Coordinates of the B point are B(k * left, k * bottom, zfar), where k = zfar/znear.

Arguments

• float left - Left coordinate of the near clipping plane relatively to the center.
• float right - Right coordinate of the near clipping plane relatively to the center.
• float bottom - Bottom coordinate of the near clipping plane relatively to the center.
• float top - Top coordinate of the near clipping plane relatively to the center.
• float znear - Distance to the near depth clipping plane.
• float zfar - Distance to the farther depth clipping plane.

Return value

Variable inverse ( Variable matrix ) #

Arguments

• Variable matrix - Matrix to be inverted (mat3, mat4 or dmat4).

Return value

quat inverse ( quat q ) #

Arguments

• quat q - Quaternion to be inverted.

Return value

Variable inverse4 ( mat4 matrix ) #

Arguments

• mat4 matrix - Matrix to be inverted.

Return value

Variable lookAt ( Variable position, Variable target, vec3 up, int axis = AXIS_NZ ) #

Arguments

• Variable position - Position coordinates of the eye point (vec3 or dvec3).
• Variable target - Position coordinates of the target point (vec3 or dvec3).
• vec3 up - Direction of the up vector.
• int axis - Axis along which the forward direction vector is pointed. The default is negative Z.

Return value

• mat4, if the first input argument is vec3
• dmat4 if the first argument is dvec3

Variable obliqueProjection ( mat4 projection, vec4 plane ) #

Arguments

• mat4 projection - Projection matrix.
• vec4 plane - Clipping plane.

Return value

Variable orthoTangent ( vec3 tangent, vec3 binormal, vec3 normal ) #

Arguments

• vec3 tangent - Tangent vector.
• vec3 binormal - Binormal vector.
• vec3 normal - Normal vector.

Return value

Examples

The following example demonstrates how to convert the mesh tangent vector to the normal and binormal vectors. The mesh tangent vector is calculated via the orthoTangent() function.

vec3 t = vec3(1.0f,0.0f,0.0f); // the tangent basis: tangent vector
vec3 b = vec3(0.0f,1.0f,0.0f); // binormal vector
vec3 n = vec3(0.0f,0.0f,1.0f); // normal vector
vec4 tangent = orthoTangent(t,b,n); // this is the mesh compressed tangent vector

quat compact_tangent_quat = quat(tangent); // convert vec4 to quat

log.message("b: %s\n",typeinfo(compact_tangent_quat.binormal)); // get the col1 (binormal) with w normalization
log.message("n: %s\n\n",typeinfo(compact_tangent_quat.normal)); // get the col2 (normal) with w normalization

// manually normalize the w component of the quaternion
// and convert the quaternion into the matrix
mat4 compact_tangent_mat = mat4(normalize3(compact_tangent_quat)); // when the w component of the quaternion is normalized, the sign of binormal will be lost for the matrix

// get the col1 and col2 of the matrix
log.message("b: %s\n",typeinfo(compact_tangent_mat.binormal * tangent.w)); // you should multiply the binormal by the tangent w component to restore the sign
log.message("n: %s\n",typeinfo(compact_tangent_mat.normal));

Variable orthoTangent ( vec4 tangent, vec3 normal ) #

Arguments

• vec4 tangent - Tangent vector: the first 3 components are coordinates of the tangent vector, and the fourth w component is the sign of the binormal.
• vec3 normal - Normal vector.

Return value

mat4 ortho ( float left, float right, float bottom, float top, float znear, float zfar ) #

Arguments

• float left - Left vertical clipping plane.
• float right - Right vertical clipping plane.
• float bottom - Bottom horizontal clipping plane.
• float top - Top horizontal clipping plane.
• float znear - Nearest depth clipping plane.
• float zfar - Farther depth clipping plane.

Return value

Variable orthonormalize ( Variable v ) #

Arguments

• Variable v - Matrix (either mat4 or dmat4) to be orthonormalized.

Return value

mat4 perspective ( float fov, float aspect, float znear, float zfar ) #

Arguments

• float fov - Field of view angle.
• float aspect - Aspect ratio. The aspect ratio is the ratio of width to height.
• float znear - Nearest depth clipping plane.
• float zfar - Farther depth clipping plane.

Return value

Variable reflect ( Variable plane ) #

Arguments

• Variable plane - Reflection plane.

Return value

Variable reflect ( Variable v0, Variable v1 ) #

Arguments

• Variable v0 - Vector to be reflected (vec3 or dvec3)
• Variable v1 - Normal vector to the reflection plane (of the same type as v0 vector).

Return value

mat4 rotateX ( float angle ) #

Arguments

• float angle - Rotation angle, in degrees.

Return value

mat4 rotateY ( float angle ) #

Arguments

• float angle - Rotation angle, in degrees.

Return value

mat4 rotateZ ( float angle ) #

Arguments

• float angle - Rotation angle, in degrees.

Return value

mat4 rotate ( float x, float y, float z, float angle ) #

Arguments

• float x - X component of rotation axis.
• float y - Y component of rotation axis.
• float z - Z component of rotation axis.
• float angle - Rotation angle, in degrees.

Return value

mat4 rotate ( vec3 axis, float angle ) #

Arguments

• vec3 axis - Rotation axis. This vector does not have to be normalized.
• float angle - Rotation angle, in degrees.

Return value

Variable rotateTowards ( Variable source, Variable target, float max_angle ) #

Arguments

• Variable source - Source vector/quaternion. Can be of the following types:
  • vec3
  • quat
• Variable target - Target vector/quaternion. Can be of the following types:
  • vec3
  • quat
• float max_angle - Angular step, in degrees. If a negative value is specified, 0 will be used instead.

Return value

• vec3 for vec3 arguments
• quat for quat arguments

Variable rotation ( Variable v ) #

Arguments

• Variable v - Source, can be of quat, mat4 or dmat4 type.

Return value

mat4 scale ( float x, float y, float z ) #

Arguments

• float x - X component of the scaling vector.
• float y - Y component of the scaling vector.
• float z - Z component of the scaling vector.

Return value

mat4 scale ( vec3 vector ) #

Arguments

• vec3 vector - Scaling vector.

Return value

Variable setTo ( Variable position, Variable target, vec3 up, int axis = AXIS_NZ ) #

Arguments

• Variable position - Position of the eye point (vec3 or dvec3).
• Variable target - Position of the target point (vec3 or dvec3).
• vec3 up - Direction of the up vector.
• int axis - Axis along which the forward direction vector is pointed. The default is negative Z.

Return value

• mat4, if the first input argument is vec3
• dmat4 if the first argument is dvec3

Variable symmetryProjection ( mat4 projection ) #

Arguments

• mat4 projection - Projection matrix.

Return value

Variable translate ( Variable v ) #

Arguments

• Variable v - Translation vector (either vec3 or dvec3).

Return value

• mat4, if the input argument is vec3
• dmat4 if the argument is dvec3

Variable translate ( Variable x, Variable y, Variable z ) #

Arguments

• Variable x - X component of the translation vector (int, float or double).
• Variable y - Y component of the translation vector (int, float or double).
• Variable z - Z component of the translation vector (int, float or double).

Return value

• mat4, if the first input argument is int or float
• dmat4, if the first argument is double

mat4 transpose ( mat4 matrix ) #

Arguments

• mat4 matrix - Argument.

Return value

Variable transpose3 ( mat4 matrix ) #

Arguments

• mat4 matrix - Matrix, a part of which will be transposed.

Return value