MODULE; IMPORT R2, Math; PROCEDURE Matrix2D Scale (READONLY sx, sy: REAL): T = BEGIN RETURN T{sx, 0.0, 0.0, sy, 0.0, 0.0}; END Scale; PROCEDURETranslate (READONLY tx, ty: REAL): T = BEGIN RETURN T{1.0, 0.0, 0.0, 1.0, tx, ty}; END Translate; PROCEDURERotate (READONLY theta: REAL): T = VAR s := FLOAT(Math.sin(FLOAT(theta, LONGREAL))); c := FLOAT(Math.cos(FLOAT(theta, LONGREAL))); BEGIN RETURN T{ c, s, -s, c, 0.0, 0.0}; END Rotate; PROCEDUREConcat (READONLY m, n: T): T = BEGIN RETURN T{m[0] * n[0] + m[1] * n[2], m[0] * n[1] + m[1] * n[3], m[2] * n[0] + m[3] * n[2], m[2] * n[1] + m[3] * n[3], m[4] * n[0] + m[5] * n[2] + n[4], m[4] * n[1] + m[5] * n[3] + n[5]}; END Concat;
from maple:[ a b 0 ] [ ] A := [ c d 0 ] [ ] [ e f 1 ]
inverse(A); [ d b ] [ --------- - --------- 0 ] [ a d - c b a d - c b ] [ ] [ c a ] [ - --------- --------- 0 ] [ a d - c b a d - c b ] [ ] [ c f - d e a f - b e ] [ --------- - --------- 1 ] [ a d - c b a d - c b ]
PROCEDUREInverse (READONLY m: T): T = VAR det := m[0] * m[3] - m[1] * m[2]; BEGIN RETURN T{ m[3] / det, -m[1] / det, -m[2] / det, m[0] / det, (m[2] * m[5] - m[3] * m[4]) / det, (m[1] * m[4] - m[0] * m[5]) / det}; END Inverse; PROCEDUREConcat3 (READONLY l, m, n: T): T = BEGIN RETURN T{(l[0] * m[0] + l[1] * m[2]) * n[0] + (l[0] * m[1] + l[1] * m[3]) * n[2], (l[0] * m[0] + l[1] * m[2]) * n[1] + (l[0] * m[1] + l[1] * m[3]) * n[3], (l[2] * m[0] + l[3] * m[2]) * n[0] + (l[2] * m[1] + l[3] * m[3]) * n[2], (l[2] * m[0] + l[3] * m[2]) * n[1] + (l[2] * m[1] + l[3] * m[3]) * n[3], (l[4] * m[0] + l[5] * m[2] + m[4]) * n[0] + (l[4] * m[1] + l[5] * m[3] + m[5]) * n[2] + n[4], (l[4] * m[0] + l[5] * m[2] + m[4]) * n[1] + (l[4] * m[1] + l[5] * m[3] + m[5]) * n[3] + n[5]}; END Concat3; PROCEDURETransform (READONLY m: T; READONLY p: R2.T): R2.T = BEGIN RETURN R2.T{p[0] * m[0] + p[1] * m[2] + m[4], p[0] * m[1] + p[1] * m[3] + m[5]}; END Transform; BEGIN END Matrix2D.