Vector Math

Namespace: dmVMath Language: C++ Type: Defold C++ File: vmath.h Source: engine/dlib/src/dmsdk/dlib/vmath.h Include: dmsdk/dlib/vmath.h

Vector Math functions.

API

AppendScale

Type: FUNCTION post multiply scale

Parameters

• m (Matrix4) - the matrix
• v (Vector3) - the scale vector

Returns

• r (Matrix4) - the scaled vector

Cross

Type: FUNCTION cross product between two vectors

Parameters

• a (Vector3) - the operand
• b (Vector3) - the dividend

Returns

• v (Vector3) - the result vector

DivPerElem

Type: FUNCTION Divide two vectors per element: Vector3(a.x/b.x, a.y/b.y, a.z/b.z)

Parameters

• a (Vector3) - the operand
• b (Vector3) - the dividend

Returns

• v (Vector3) - the result vector

DivPerElem

Type: FUNCTION Divide two vectors per element: Vector3(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w)

Parameters

• a (Vector4) - the operand
• b (Vector4) - the dividend

Returns

• v (Vector4) - the result vector

Dot

Type: FUNCTION dot product between two vectors

Parameters

• a (Vector3) - the first vector
• b (Vector3) - the second vector

Returns

• dot_product (float) - the dot product

Dot

Type: FUNCTION dot product between two vectors

Parameters

• a (Vector4) - the first vector
• b (Vector4) - the second vector

Returns

• dot_product (float) - the dot product

EulerToQuat

Type: FUNCTION Converts euler angles (x, y, z) in degrees into a quaternion The error is guaranteed to be less than 0.001.

Parameters

• xyz (Vector3) - rotation (deg)

Inverse

Type: FUNCTION inverse matrix

Parameters

• m (Matrix3) - the rotation

Returns

• r (Matrix3) - the transposed matrix

Inverse

Type: FUNCTION inverse matrix

Parameters

• m (Matrix4) - the rotation

Returns

• r (Matrix4) - the transposed matrix

Length

Type: FUNCTION calculate length of a vector

Parameters

• v (Vector3) - the vector

Returns

• length (float) - the length

Length

Type: FUNCTION calculate length of a vector

Parameters

• v (Vector3) - the vector

Returns

• length (float) - the length

Length

Type: FUNCTION calculate length of a quaternion

Parameters

• v (Quat) - the quaternion

Returns

• length (float) - the length

Length

Type: FUNCTION calculate squared length of a vector

Parameters

• v (Vector3) - the vector

Returns

• length (float) - the squared length

Length

Type: FUNCTION calculate squared length of a vector

Parameters

• v (Vector4) - the vector

Returns

• length (float) - the squared length

Length

Type: FUNCTION calculate squared length of a quaternion

Parameters

• v (Quat) - the vector

Returns

• length (float) - the squared length

Lerp

Type: FUNCTION linear interpolate between two vectors

Notes

• Does not clamp t to between 0 and 1

Parameters

• t (float) - the unit time
• a (Vector3) - the start vector (t == 0)
• b (Vector3) - the end vector (t == 1)

Returns

• v (Vector3) - the result vector v = a + (b - a) * t

Examples

dmVMath::Vector3 v0 = dmVMath::Lerp(0.0f, a, b); // v0 == a
dmVMath::Vector3 v1 = dmVMath::Lerp(1.0f, a, b); // v1 == b
dmVMath::Vector3 v2 = dmVMath::Lerp(2.0f, a, b); // v2 == a + (b-a) * 2.0f

Lerp

Type: FUNCTION linear interpolate between two vectors

Notes

• Does not clamp t to between 0 and 1

Parameters

• t (float) - the unit time
• a (Vector4) - the start vector (t == 0)
• b (Vector4) - the end vector (t == 1)

Returns

• v (Vector4) - the result vector v = a + (b - a) * t

Examples

dmVMath::Vector4 v0 = dmVMath::Lerp(0.0f, a, b); // v0 == a
dmVMath::Vector4 v1 = dmVMath::Lerp(1.0f, a, b); // v1 == b
dmVMath::Vector4 v2 = dmVMath::Lerp(2.0f, a, b); // v2 == a + (b-a) * 2.0f

Matrix3

Type: TYPEDEF A 3x3 matrix

Notes

• 16 byte aligned
• Implemented as 3 x Vector3
• Column major
• Currently scalar implementation is used on most platforms

Matrix4

Type: TYPEDEF A 4x4 matrix

Notes

• 16 byte aligned
• Implemented as 4 x Vector4
• Column major
• Currently scalar implementation is used on most platforms

MulPerElem

Type: FUNCTION Multiply two vectors per element: Vector3(a.x * b.x, a.y * b.y, a.z * b.z)

Parameters

• a (Vector3) - the first vector
• b (Vector3) - the second vector

Returns

• v (Vector3) - the result vector

MulPerElem

Type: FUNCTION Multiply two vectors per element: Vector3(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w)

Parameters

• a (Vector4) - the first vector
• b (Vector4) - the second vector

Returns

• v (Vector4) - the result vector

MulPerElem

Type: FUNCTION Return absolute value per element: Vector3(abs(v.x), abs(v.y), abs(v.z))

Parameters

• v (Vector3) - the vector

Returns

• r (Vector3) - the result vector

MulPerElem

Type: FUNCTION Returns the conjugate of the quaternion: conj = -q

Parameters

• q (Quat) - the quaternions

Returns

• r (Quat) - the result

Normalize

Type: FUNCTION normalize a vector to length 1

Parameters

• v (Vector3) - the vector

Returns

• n (Vector3) - the normalized vector

Normalize

Type: FUNCTION normalize a vector to length 1

Parameters

• v (Vector4) - the vector

Returns

• n (Vector4) - the normalized vector

Normalize

Type: FUNCTION normalize a quaternion to length 1

Parameters

• v (Quat) - the quaternion

Returns

• n (Quat) - the normalized quaternion

OrthoInverse

Type: FUNCTION Compute the inverse of a 4x4 matrix, which is expected to be an affine matrix with an orthogonal upper-left 3x3 submatrix

Parameters

• m (Matrix4) - the rotation

Returns

• r (Matrix4) - the transposed matrix

Point3

Type: TYPEDEF A 3-tuple (with 4-th element always set to 1)

Notes

• 16 byte aligned
• Always size of 4 float32
• Currently scalar implementation is used on most platforms

Examples

dmVMath::Point3 p = dmVMath::Point3(x, y, z); // Create new point
float length_squared = p.getX() * p.getX() + p.getY() * p.getY() + p.getZ() * p.getZ();

Quat

Type: TYPEDEF A 4-tuple representing a rotation rotation. The xyz represents the axis, and the w represents the angle.

Notes

• 16 byte aligned
• Always size of 4 float32
• Currently scalar implementation is used on most platforms

Examples

dmVMath::Quat p = dmVMath::Quat(x, y, z, w); // Create new rotation. W is the angle

QuatFromAngle

Type: FUNCTION construct a quaternion from an axis index and angle

Parameters

• axis_index (uint32_t) - index of the rotation axis
• radians (float) - angle of rotation in radians

Returns

• q (Quat) - quaternion describing the rotation

QuatToEuler

Type: FUNCTION Converts a quaternion into euler angles (r0, r1, r2), based on YZX rotation order. To handle gimbal lock (singularity at r1 ~ +/- 90 degrees), the cut off is at r0 = +/- 88.85 degrees, which snaps to +/- 90. The provided quaternion is expected to be normalized. The error is guaranteed to be less than +/- 0.02 degrees

Parameters

• q0 (float) - first imaginary axis
• q1 (float) - second imaginary axis
• q2 (float) - third imaginary axis
• q3 (float) - real part

Returns

• euler (Vector3) - euler angles in degrees

Rotate

Type: FUNCTION rotate vector using quaternion

Parameters

• q (Quat) - the rotation
• v (Vector3) - the vector

Returns

• r (Vector3) - the rotated vector

Slerp

Type: FUNCTION spherical linear interpolate between two vectors

Notes

• Does not clamp t to between 0 and 1
• Unpredicatable results if a and b point in opposite direction

Parameters

• t (float) - the unit time
• a (Vector3) - the start vector (t == 0)
• b (Vector3) - the end vector (t == 1)

Returns

• v (Vector3) - the result vector

Slerp

Type: FUNCTION spherical linear interpolate between two vectors

Notes

• Does not clamp t to between 0 and 1
• Unpredicatable results if a and b point in opposite direction

Parameters

• t (float) - the unit time
• a (Vector4) - the start vector (t == 0)
• b (Vector4) - the end vector (t == 1)

Returns

• v (Vector4) - the result vector

Slerp

Type: FUNCTION Interpolates along the shortest path between two quaternions

Notes

• Does not clamp t to between 0 and 1

Parameters

• t (float) - the unit time
• a (Quat) - the start vector (t == 0)
• b (Quat) - the end vector (t == 1)

Returns

• v (Quat) - the result vector

Transpose

Type: FUNCTION transpose matrix

Parameters

• m (Matrix3) - the rotation

Returns

• r (Matrix3) - the transposed matrix

Transpose

Type: FUNCTION transpose matrix

Parameters

• m (Matrix4) - the rotation

Returns

• r (Matrix4) - the transposed matrix

Vector3

Type: TYPEDEF A 3-tuple (with 4-th element always set to 0)

Notes

• 16 byte aligned
• Always size of 4 float32
• Currently scalar implementation is used on most platforms

Examples

dmVMath::Vector3 p = dmVMath::Vector3(x, y, z); // Create new vector
float length_squared = p.getX() * p.getX() + p.getY() * p.getY() + p.getZ() * p.getZ();

Vector4

Type: TYPEDEF A 4-tuple

Notes

• 16 byte aligned
• Always size of 4 float32
• Currently scalar implementation is used on most platforms

Examples

dmVMath::Vector4 p = dmVMath::Vector4(x, y, z, w); // Create new vector
float length_squared = p.getX() * p.getX() + p.getY() * p.getY() + p.getZ() * p.getZ() + p.getW() * p.getW();