DIRECTORY Cubic2, Cubic2Extras, Vector2, Imager; Cubic2Impl: CEDAR PROGRAM IMPORTS Vector2 EXPORTS Cubic2, Cubic2Extras = { OPEN Vector2, Cubic2; VEC: TYPE = Imager.VEC; CoeffsToBezier: PUBLIC PROC [coeffs: Coeffs] RETURNS [bezier: Bezier] = { bezier.b0 _ coeffs.c0; bezier.b1 _ Add[coeffs.c0,Div[coeffs.c1,3]]; bezier.b2 _ Add[bezier.b1,Div[Add[coeffs.c1,coeffs.c2],3]]; bezier.b3 _ Add[Add[Add[coeffs.c0,coeffs.c1],coeffs.c2],coeffs.c3]; RETURN[bezier]; }; BezierToCoeffs: PUBLIC PROC [bezier: Bezier] RETURNS [coeffs: Coeffs] = { t: VEC _ Mul[Sub[bezier.b2,bezier.b1],3]; coeffs.c0 _ bezier.b0; coeffs.c1 _ Mul[Sub[bezier.b1,bezier.b0],3]; coeffs.c2 _ Sub[t,coeffs.c1]; coeffs.c3 _ Sub[bezier.b3,Add[bezier.b0,t]]; RETURN[coeffs]; }; AlphaSplit: PUBLIC PROC [bezier: Bezier, alpha: REAL] RETURNS[Bezier,Bezier] = { Fraction: PROC[q,r: VEC, alpha: REAL, beta: REAL] RETURNS [VEC] = { RETURN[[q.x*beta+r.x*alpha, q.y*beta+r.y*alpha]] }; a,b,c,ab,bc,p: VEC; oneMinusAlpha: REAL; oneMinusAlpha _ 1.0-alpha; a _ Fraction[bezier.b0, bezier.b1, alpha, oneMinusAlpha]; b _ Fraction[bezier.b1, bezier.b2, alpha, oneMinusAlpha]; c _ Fraction[bezier.b2, bezier.b3, alpha, oneMinusAlpha]; ab _ Fraction[a, b, alpha, oneMinusAlpha]; bc _ Fraction[b, c, alpha, oneMinusAlpha]; p _ Fraction[ab, bc, alpha, oneMinusAlpha]; RETURN[[bezier.b0, a, ab, p],[p, bc, c, bezier.b3]]; }; Split: PUBLIC PROC [bezier: Bezier] RETURNS [Bezier,Bezier] = { a,b,c,ab,bc,p: VEC; Mid: PROC [u,v: VEC] RETURNS [VEC] = INLINE { RETURN[[(u.x+v.x)/2,(u.y+v.y)/2]] }; a _ Mid[bezier.b0,bezier.b1]; b _ Mid[bezier.b1,bezier.b2]; c _ Mid[bezier.b2,bezier.b3]; ab _ Mid[a,b]; bc _ Mid[b,c]; p _ Mid[ab,bc]; RETURN[[bezier.b0, a, ab, p],[p, bc, c, bezier.b3]]; }; Flat: PUBLIC PROC [bezier: Bezier, epsilon: REAL] RETURNS [BOOL] = { dx,dy: REAL; d1,d2,d,bl,bh: VEC; oh: VEC=[epsilon, epsilon]; bh _ Vector2.Add[UpperRight[bezier.b0,bezier.b3],oh]; bl _ Vector2.Sub[LowerLeft[bezier.b0,bezier.b3],oh]; IF ~In[bezier.b1,bl,bh] OR ~In[bezier.b2,bl,bh] THEN RETURN[FALSE]; d _ Vector2.Sub[bezier.b3,bezier.b0]; dx _ ABS[d.x]; dy _ ABS[d.y]; IF dx+dy < epsilon THEN RETURN[TRUE]; d1 _ Vector2.Sub[bezier.b1,bezier.b0]; d2 _ Vector2.Sub[bezier.b2,bezier.b0]; IF dy < dx THEN { dydx: REAL _ d.y/d.x; RETURN[ABS[d2.y-d2.x*dydx]Kšœœ œœ ˜.Kšœ˜—Kšœ˜K˜—…— t"