Function translate

Append a translation transform inferred from arguments to the matrix m. This is equivalent to the expression 

translation(...) * m
but actually save computation by knowing where the ones and zeros are in a pure translation matrix.

M translate(M, X, Y) (
  in M m,
  in X x,
  in Y y
)
if (isMat!(3, 3, M) && allSatisfy!(isNumeric, X, Y));

M translate(M, X, Y) (
  in M m,
  in X x,
  in Y y
)
if (isMat!(2, 3, M) && allSatisfy!(isNumeric, X, Y));

M translate(M, V) (
  in M m,
  in V v
)
if ((isMat!(2, 3, M) || isMat!(3, 3, M)) && isVec!(2, V));

M translate(M, X, Y, Z) (
  in M m,
  in X x,
  in Y y,
  in Z z
)
if (isMat!(4, 4, M) && allSatisfy!(isNumeric, X, Y, Z));

M translate(M, X, Y, Z) (
  in M m,
  in X x,
  in Y y,
  in Z z
)
if (isMat!(3, 4, M) && allSatisfy!(isNumeric, X, Y, Z));

M translate(M, V) (
  in M m,
  in V v
)
if ((isMat!(3, 4, M) || isMat!(4, 4, M)) && isVec!(3, V));

Example

import gfx.math.approx : approxUlp;

immutable m = DMat3( 1, 2, 3, 4, 5, 6, 7, 8, 9 );

immutable expected = translation(7, 12) * m;  // full multiplication
immutable result = translate(m, 7, 12);       // simplified multiplication

assert (approxUlp(expected, result));

Example

import gfx.math.approx : approxUlp;

immutable m = DMat4( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 );

immutable expected = translation(7, 12, 18) * m;  // full multiplication
immutable result = translate(m, 7, 12, 18);       // simplified multiplication

assert (approxUlp(expected, result));