12.6 Maths

These functions are optimised for 3D graphics, and the collision of computer science and maths is apparent here, so vectors representing "vectors" are in this context taken to be 3 elements long, quaternions are vectors of length 4, and matrices are vectors of 16 elements long.

Example

12.6.1 (vmul vector number)

Returns

result-vector

Description

Multiplies a vector by a number

Example

      (vmul (vector 1 2 3) 2)
     

12.6.2 (vadd vector vector)

Returns

result-vector

Description

Adds two vectors together

Example

      (vadd (vector 1 2 3) (vector 1 2 3))
     

12.6.3 (vsub vector vector)

Returns

result-vector

Description

Subtracts a vector from another

Example

      (vsub (vector 1 2 3) (vector 1 2 3))
     

12.6.4 (vdiv vector number)

Returns

result-vector

Description

Divides a vector by a number

Example

      (vdiv (vector 1 2 3) 2)
     

12.6.5 (vtransform vector matrix)

Returns

result-vector

Description

Multiplies (transforms) a vector by a matrix

Example

      (vtransform (vector 0 1 0) (mrotate (vector 90 0 0)))
     

12.6.6 (vtransform-rot vector matrix)

Returns

result-vector

Description

Multiplies (transforms) a vector by a matrix, but leaves out the translation part. For operations involving normals.

Example

      (vtransform-rot (vector 0 1 0) (mrotate (vector 90 0 0)))
     

12.6.7 (vnormalise vector)

Returns

result-vector

Description

Returns the normalised form of the vector (length=1)

Example

      (vtransform-rot (vector 0 1 0) (mrotate (vector 90 0 0)))
     

12.6.8 (vdot vector vector)

Returns

result-number

Description

Returns the dot product of two vectors

Example

      (vdot (vector 0 1 0) (vector 1 0 0))
     

12.6.9 (vmag vector)

Returns

result-number

Description

Returns the magnitude, or length of the vector

Example

      (vmag (vector 0 1 1))
     

12.6.10 (vdist vector vector)

Returns

result-number

Description

Treating the vectors as points, returns the distance between them

Example

      (vdist (vector 100 100 0) (vector 0 0 100))
     

12.6.11 (vcross vector vector)

Returns

result-vector

Description

Returns the cross product of two vectors

Example

      (vcross (vector 100 100 0) (vector 0 0 100))
     

12.6.12 (mmul matrix-vector matrix-vector)

Returns

matrix-vector

Description

Multiplies two matrices together

Example

      (vmul (mtranslate (vector 1 0 0)) (mrotate (vector 0 90 0)))
     

12.6.13 (madd matrix-vector matrix-vector)

Returns

matrix-vector

Description

Adds two matrices together

Example

      (vadd (mtranslate (vector 1 0 0)) (mrotate (vector 0 90 0)))
     

12.6.14 (msub matrix-vector matrix-vector)

Returns

matrix-vector

Description

Subtracts a matrix from another

Example

      (vsub (mtranslate (vector 1 0 0)) (mrotate (vector 0 90 0)))
     

12.6.15 (mdiv matrix-vector matrix-vector)

Returns

matrix-vector

Description

Divides a matrix by another

Example

      (vdiv (mtranslate (vector 1 0 0)) (mrotate (vector 0 90 0)))
     

12.6.16 (mident)

Returns

matrix-vector

Description

Returns the identity matrix

Example

      (mident)
     

12.6.17 (mtranslate vector)

Returns

matrix-vector

Description

Returns a matrix representing the specified transform

Example

      (mtransform (vector 100 0 0))
     

12.6.18 (mrotate vector)

Returns

matrix-vector

Description

Returns a matrix representing the specified rotation. Accepts a vector of euler angles, or a quaternion.

Example

      (mrotate (vector 0 45 0))
     

12.6.19 (mscale vector)

Returns

matrix-vector

Description

Returns a matrix representing the specified scaling.

Example

      (mscale (vector 0.5 2 0.5))
     

12.6.20 (mtranspose matrix-vector)

Returns

matrix-vector

Description

Returns the transpose of the input vector

Example

      (mtranspose (mident))
     

12.6.21 (minverse matrix-vector)

Returns

matrix-vector

Description

Returns the inverse of the input vector

Example

      (minverse (mscale (vector 0.5 2 0.5)))
     

12.6.22 (maim aim-vector up-vector)

Returns

matrix-vector

Description

Returns a matrix representing an aiming rotation so that the x axis points down the aim direction, and the y axis points up the up vector. Probably suffers from gimbal lock.

Example

      (maim (vector 0 0 1) (vector 0 1 0))
     

12.6.23 (qaxisangle axis-vector angle-number)

Returns

quaternion-vector

Description

Returns the quaternion representing rotation of angle degrees about the specified axis.

Example

      (qaxisangle (vector 0 1 0) 45)
     

12.6.24 (qmul quaternion-vector quaternion-vector)

Returns

quaternion-vector

Description

Multiplies two quaternions together.

Example

      (qmul (qaxisangle (vector 0 1 0) 45) (qaxisangle (vector 0 0 1) 180))
     

12.6.25 (qnormalise quaternion-vector)

Returns

quaternion-vector

Description

Normalises a quaternion.

Example

      (qnormalise (qaxisangle (vector 0 19 0) 45))
     

12.6.26 (qtomatrix quaternion-vector)

Returns

matrix-vector

Description

Converts a quaternion into a rotation matrix.

Example

      (qtomatrix (qaxisangle (vector 0 1 0) 45))
     

12.6.27 (qconjugate quaternion-vector)

Returns

quaternion-vector

Description

Conjugatea a quaternion.

Example

      (qconjugate (qaxisangle (vector 0 1 0) 45))