Constant e.
Machine float epsilon, pow(2, -52).
Constant pi.
Applies abs function to each component.
Applies abs function to each component.
an integer vector argument.
a vector with components set to absolute values of components of u.
Applies abs function to each component.
Applies abs function to each component.
an integer vector argument.
a vector with components set to absolute values of components of u.
Applies abs function to each component.
Applies abs function to each component.
an integer vector argument.
a vector with components set to absolute values of components of u.
Returns an absolute value of the argument.
Returns an absolute value of the argument.
an integer argument.
an absolute value of the agument.
The matrix must represent non-scaling rotation to achieve the desired result.
The matrix must represent non-scaling rotation to achieve the desired result. If the matrix represents 0 degree rotation, then rotation axis is undefined, in this case the UnitX axis is chosen.
The quaternion must have unit norm to achieve the desired result.
The quaternion must have unit norm to achieve the desired result. If quaternion represents 0 degree rotation, then rotation axis is not defined, in this case the UnitX axis is chosen.
Applies clamp function to each component.
Applies clamp function to each component.
an integer vector argument.
a vector with components used as lower bound (inclusive).
a vector with components used as upper bound (inclusive).
a vector with components set to clamp(u.c, minVal.c, maxVal.c)
for each component c.
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
an integer vector argument.
the lower bound (inclusive).
the upper bound (inclusive).
a vector with components clamped to [minValue, maxValue].
Applies clamp function to each component.
Applies clamp function to each component.
an integer vector argument.
a vector with components used as lower bound (inclusive).
a vector with components used as upper bound (inclusive).
a vector with components set to clamp(u.c, minVal.c, maxVal.c)
for each component c.
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
an integer vector argument.
the lower bound (inclusive).
the upper bound (inclusive).
a vector with components clamped to [minValue, maxValue].
Applies clamp function to each component.
Applies clamp function to each component.
an integer vector argument.
a vector with components used as lower bound (inclusive).
a vector with components used as upper bound (inclusive).
a vector with components set to clamp(u.c, minVal.c, maxVal.c)
for each component c.
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
Clamps components to the range from minValue (inclusive) to maxValue (inclusive).
an integer vector argument.
the lower bound (inclusive).
the upper bound (inclusive).
a vector with components clamped to [minValue, maxValue].
Clamps a value to a given range.
Clamps a value to a given range. Note: the result is undefined if minVal > maxVal.
an integer value to clamp.
the lower bound (inclusive).
the upper bound (inclusive).
one of the following:
Performs component-wise equal comparison.
Performs component-wise equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c == v.c)
for each component c.
Performs component-wise equal comparison.
Performs component-wise equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c == v.c)
for each component c.
Performs component-wise equal comparison.
Performs component-wise equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c == v.c)
for each component c.
Equivalent to x - floor(x)
Performs component-wise greater than comparison.
Performs component-wise greater than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c > v.c)
for each component c.
Performs component-wise greater than comparison.
Performs component-wise greater than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c > v.c)
for each component c.
Performs component-wise greater than comparison.
Performs component-wise greater than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c > v.c)
for each component c.
Performs component-wise greater than or equal comparison.
Performs component-wise greater than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c >= v.c)
for each component c.
Performs component-wise greater than or equal comparison.
Performs component-wise greater than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c >= v.c)
for each component c.
Performs component-wise greater than or equal comparison.
Performs component-wise greater than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c >= v.c)
for each component c.
This method is here for completness.
This method is here for completness. Normally you should work with
unit quaternions (norm(q) == 1
), and in this case
inverse(q) == conjugate(q)
.
This method is equivalent to casting the matrix to 4x4, inverting it and then casting the result back to 4x3.
This method is equivalent to casting the matrix to 4x4, inverting it
and then casting the result back to 4x3.
This is a general matrix inverse. You can invert transofrmations quicker by using Transform3d.inverse(scale, rotation, translation). A rotation matrix that does not scale can be inverted even faster by using transpose. In the latter case you can avoid inverse alltogether by using transpose multiplication: instead of multiplying a matrix by a vectors (M*v), you can multiply the vector by the matrix (v*M).
If matrix determinant is zero the result is undefined.
This method is equivalent to casting the matrix to 3x3, inverting it and then casting the result back to 3x2.
This method is equivalent to casting the matrix to 3x3, inverting it
and then casting the result back to 3x2.
This is a general matrix inverse. You can invert transofrmations quicker by using Transform2d.inverse(scale, rotation, translation). A rotation matrix that does not scale can be inverted even faster by using transpose. In the latter case you can avoid inverse alltogether by using transpose multiplication: instead of multiplying a matrix by a vectors (M*v), you can multiply the vector by the matrix (v*M).
If matrix determinant is zero the result is undefined.
This is a general matrix inverse.
This is a general matrix inverse. You can invert transofrmations quicker by using Transform3d.inverse(scale, rotation, translation). A rotation matrix that does not scale can be inverted even faster by using transpose. In the latter case you can avoid inverse alltogether by using transpose multiplication: instead of multiplying a matrix by a vectors (M*v), you can multiply the vector by the matrix (v*M).
If matrix determinant is zero the result is undefined.
This is a general matrix inverse.
This is a general matrix inverse. You can invert transofrmations quicker by using Transform3d.inverse(scale, rotation, translation). A rotation matrix that does not scale can be inverted even faster by using transpose. In the latter case you can avoid inverse alltogether by using transpose multiplication: instead of multiplying a matrix by a vectors (M*v), you can multiply the vector by the matrix (v*M).
If matrix determinant is zero the result is undefined.
If matrix determinant is zero the result is undefined.
Must be an orthogonal matrix (matrix that represents an unscaled rotation) to achieve the desired result.
Must be an orthogonal matrix (matrix that represents an unscaled rotation) to achieve the desired result.
Performs component-wise less than comparison.
Performs component-wise less than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c < v.c)
for each component c.
Performs component-wise less than comparison.
Performs component-wise less than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c < v.c)
for each component c.
Performs component-wise less than comparison.
Performs component-wise less than comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c < v.c)
for each component c.
Performs component-wise less than or equal comparison.
Performs component-wise less than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c <= v.c)
for each component c.
Performs component-wise less than or equal comparison.
Performs component-wise less than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c <= v.c)
for each component c.
Performs component-wise less than or equal comparison.
Performs component-wise less than or equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c <= v.c)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to max(u.c, v.c)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
a vector with components set to max(c, s)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to max(u.c, v.c)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
a vector with components set to max(c, s)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to max(u.c, v.c)
for each component c.
Applies max function to each component.
Applies max function to each component.
an integer vector argument.
a vector with components set to max(c, s)
for each component c.
Returns the larger one of two arguments.
Returns the larger one of two arguments.
an integer argument.
an integer argument.
the largest argument.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to min(u.c, v.c)
for each component c.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
a vector with components set to min(c, s)
for each component c.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to min(u.c, v.c)
for each component c.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
a vector with components set to min(c, s)
for each component c.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
an integer vector argument.
a vector with components set to min(u.c, v.c)
for each component c.
Applies min function to each component.
Applies min function to each component.
an integer vector argument.
a vector with components set to min(c, s)
for each component c.
Returns the smaller one of two arguments.
Returns the smaller one of two arguments.
an integer argument.
an integer argument.
the smallest argument.
Equivalent to x - y*floor(x/y)
Separates each component of a given vector into fractional and integer parts, both parts will have the same sign as the component.
Separates each component of a given vector into fractional and integer parts, both parts will have the same sign as the component.
the vector to be separated into fractional and integer parts.
a result vector to store the integer parts of components of u.
a vector with fractional parts of components of u.
Computes normal matrix.
Computes normal matrix.
Model View Matrix.
Performs component-wise not equal comparison.
Performs component-wise not equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c != v.c)
for each component c.
Performs component-wise not equal comparison.
Performs component-wise not equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c != v.c)
for each component c.
Performs component-wise not equal comparison.
Performs component-wise not equal comparison.
an integer vector on the left-hand side of comparison.
an integer vector on the right-hand side of comparison.
a boolean vector with components set to (u.c != v.c)
for each component c.
the coordinates of the left clipping plane.
the coordinates of the right clipping plane.
the coordinates of the bottom clipping plane.
the coordinates of the top clipping plane.
the distance to the near clipping plane, negative if the plane is behind the viewer.
the distance to the far clipping plane, negative if the plane is behind the viewer.
the coordinates of the left clipping plane.
the coordinates of the right clipping plane.
the coordinates of the bottom clipping plane.
the coordinates of the top clipping plane.
the distance to the near clipping plane, must be positive, approximately log2(far/near) bits of depth buffer precision are lost.
the distance to the far clipping plane, must be positive.
field of view angle in y direction, in radians.
width/height aspect ratio.
the distance to the near clipping plane, must be positive, approximately log2(far/near) bits of depth buffer precision are lost.
the distance to the far clipping plane, must be positive.
The axis must have unit length to achieve the desired result.
The matrix must represent non-scaling rotation to achieve the desired result.
The quaternion must have unit norm to achieve the desired result.
The matrix must represent non-scaling rotation to achieve the desired result.
The axis must have unit length to achieve the desired result.
The quaternion must have unit norm to achieve the desired result.
This method creates a 2d transformation matrix that rotates a vector counterclockwise by the specified angle.
Applies sign function to each component.
Applies sign function to each component.
an integer vector argument.
a vector with components set to sign(u.c)
for each component c.
Applies sign function to each component.
Applies sign function to each component.
an integer vector argument.
a vector with components set to sign(u.c)
for each component c.
Applies sign function to each component.
Applies sign function to each component.
an integer vector argument.
a vector with components set to sign(u.c)
for each component c.
Returns the sign of the argument.
Returns the sign of the argument.
an integer argument.
one of the following: