DIRECTORY CGCubic USING [Bezier, Coeffs, BezierToCoeffs], Quadratic USING [RealRoots], RealFns USING [SqRt], Vector USING [Add, Mul, Sub, Vec], PolygonPen; PolygonPenImpl: PROGRAM IMPORTS CGCubic, Quadratic, RealFns, Vector EXPORTS PolygonPen = BEGIN Bezier: TYPE = PolygonPen.Bezier; Pen: TYPE = PolygonPen.Pen; Vec: TYPE = PolygonPen.Vec; -- a broad pen is represented as a vector, with the reference point at the origin. MoveToProc: TYPE = PolygonPen.MoveToProc; LineToProc: TYPE = PolygonPen.LineToProc; CurveToProc: TYPE = PolygonPen.CurveToProc; SimpleStroke: PUBLIC PROCEDURE [pen: Vec, curve: Bezier, moveTo: MoveToProc, lineTo: LineToProc, curveTo: CurveToProc] = BEGIN OPEN curve; moveTo[b0]; lineTo[Vector.Add[b0, pen]]; curveTo[Vector.Add[b1, pen], Vector.Add[b2, pen], Vector.Add[b3, pen]]; lineTo[b3]; curveTo[b2, b1, b0] END; BroadStroke: PUBLIC PROCEDURE [pen: Vec, curve: Bezier, moveTo: MoveToProc, lineTo: LineToProc, curveTo: CurveToProc] = BEGIN c: CGCubic.Coeffs = CGCubic.BezierToCoeffs[curve]; Stroke: PROC [t0, t1: REAL] = {SimpleStroke[pen, SubBezier[curve, t0, t1], moveTo, lineTo, curveTo]}; q2: REAL = 3*(pen.x*c.c3.y - pen.y*c.c3.x); q1: REAL = 2*(pen.x*c.c2.y - pen.y*c.c2.x); q0: REAL = pen.x*c.c1.y - pen.y*c.c1.x; dSqr: REAL = q1*q1 - 4*q0*q2; d: REAL = IF dSqr<=0 THEN 0 ELSE RealFns.SqRt[dSqr]; t0, t1: REAL; nRoots: [0..2]; [[nRoots, t0, t1]] _ Quadratic.RealRoots[q2, q1, q0]; IF nRoots>0 THEN {IF t0 < 0 THEN t0 _ 0; IF t0 > 1 THEN t0 _ 1} ELSE t0 _ 0; IF nRoots>1 THEN {IF t1 < 0 THEN t1 _ 0; IF t1 > 1 THEN t1 _ 1} ELSE t1 _ 1; IF 0 < t0 THEN Stroke[0.0, t0]; IF t0 < t1 THEN Stroke[t0, t1]; IF t1 < 1 THEN Stroke[t1, 1.0] END; SubBezier: PROCEDURE [b: CGCubic.Bezier, t0, t1: REAL] RETURNS [Bezier] = {RETURN [HighBezier[LowBezier[b, t1], t0/t1]]}; LowBezier: PROCEDURE [b: CGCubic.Bezier, t: REAL] RETURNS [Bezier] = BEGIN OPEN b; q1, q2, q3, qp1, qp2, q: Vector.Vec; q1_Interpolate[t, b0, b1]; q2_Interpolate[t, b1, b2]; q3_Interpolate[t, b2, b3]; qp1_Interpolate[t, q1, q2]; qp2_Interpolate[t, q2, q3]; q_Interpolate[t, qp1, qp2]; RETURN[[b0: b0, b1: q1, b2: qp1, b3: q]]; END; HighBezier: PROCEDURE [b: CGCubic.Bezier, t: REAL] RETURNS [Bezier] = BEGIN OPEN b; q1, q2, q3, qp1, qp2, q: Vector.Vec; q1_Interpolate[t, b0, b1]; q2_Interpolate[t, b1, b2]; q3_Interpolate[t, b2, b3]; qp1_Interpolate[t, q1, q2]; qp2_Interpolate[t, q2, q3]; q_Interpolate[t, qp1, qp2]; RETURN[[b0: q, b1: qp2, b2: q3, b3: b3]]; END; Interpolate: PROCEDURE [t: REAL, a, b: Vector.Vec] RETURNS [r: Vector.Vec] = BEGIN OPEN Vector; r _ Add[Mul[b, t], Mul[a, 1-t]]; END; Dot: PUBLIC PROCEDURE [pen: Pen, point: Vector.Vec, moveTo: MoveToProc, lineTo: LineToProc, curveTo: CurveToProc] = BEGIN n: NAT = pen.n; IF n>0 THEN moveTo[Vector.Add[pen[0], point]]; FOR i: NAT IN (0..n) DO lineTo[Vector.Add[pen[i], point]] ENDLOOP; END; Line: PUBLIC PROCEDURE [pen: Pen, startPoint, endPoint: Vector.Vec, moveTo: MoveToProc, lineTo: LineToProc, curveTo: CurveToProc] = {Stroke[pen,[startPoint, Interpolate[0.1, startPoint, endPoint], Interpolate[0.1, startPoint, endPoint], endPoint], moveTo, lineTo, curveTo]}; Stroke: PUBLIC PROCEDURE [pen: Pen, curve: Bezier, moveTo: MoveToProc, lineTo: LineToProc, curveTo: CurveToProc] = BEGIN Shifted: PROC [v: Vec] RETURNS [Bezier] = BEGIN OPEN curve, Vector; RETURN[[Add[b0, v], Add[b1, v], Add[b2, v], Add[b3, v]]] END; n: NAT = pen.n; Dot[pen, curve.b0, moveTo, lineTo, curveTo]; FOR i: NAT IN [0..n) DO OPEN curve, Vector; BroadStroke [Vector.Sub[pen[(i+1) MOD n], pen[i]], Shifted[pen[i]], moveTo, lineTo, curveTo] ENDLOOP END; END. †PolygonPenImpl.mesa Michael Plass, March 22, 1983 3:45 pm This module provides for the conversion of pen-drawn spline curves to spline-bounded outlines. The simplest kind of pen handled here is the broad pen, which is just a line segment. Polygonal-pen strokes are built up by means of multiple broad-pen strokes. The results are sent by calling procedures of the following types: ‌ت?کJکJڑœ™Jڑœ&™&Jکڑدk ک Jڑœ‌œ"ک/Jڑœ ‌œ کJڑœ‌œکJڑœ‌œک"JکJک—Jڑœپ™پJکJڑœ‌œ‌œ%‌œ کXJکJڑ‌کJکJڑœ‌œک!JکJڑœ‌œکJکJڑœ‌œدcRکnJکJڑœB™BJڑœ‌œک)Jڑœ‌œک)Jڑœ ‌œک+Jکڑدnœ‌œ‌ œZکxJڑ‌œ‌œکJکJکJکGJکJکJڑ‌œکJک—ڑںœ‌œ‌ œZکwJڑ‌کJک2ڑںœ‌œ ‌œکک,Jک——Jڑœ‌œ#ک+Jڑœ‌œ#ک+Jڑœ‌œ"ک*Jڑœ‌œکJڑ œ‌œ‌œ ‌œ‌œک4Jڑœ‌œک JکJک5ڑ‌œ ‌œ‌œ‌œک(Jڑ‌œ‌œک—Jڑ‌œکڑ‌œ ‌œ‌œ‌œک(Jڑ‌œ‌œک—Jڑ‌œکJڑ‌œ‌œکJڑ‌œ ‌œکJڑ‌œ‌œکJڑ‌œکJک—ڑں œ‌ œ‌œ‌œکIJڑœ‌œ(ک/Jک—ڑں œ‌ œ‌œ‌œکDJڑ‌œ‌œک Jک$JکJکJکJکJکJکJڑ‌œ#ک)Jڑ‌œکJک—ڑں œ‌ œ‌œ‌œکEJڑ‌œ‌œک Jک$JکJکJکJکJکJکJڑ‌œ#ک)Jڑ‌œکJک—ڑںœ‌ œ‌œ‌œکLJڑ‌œ‌œکJک Jڑ‌œکJک—ڑںœ‌œ‌ œ^کsJڑ‌کJڑœ‌œ کJڑ‌œ‌œ#ک.Jڑ ‌œ‌œ‌œ‌œ#‌œکBJڑ‌œکJک—ڑںœ‌œ‌ œmکƒJکژJک—ڑںœ‌œ‌ œZکrJڑ‌کڑںœ‌œ ‌œک)Jڑ‌œ‌œکJڑ‌œ2ک8Jڑ‌œک—Jڑœ‌œ کJک,ڑ ‌œ‌œ‌œ‌œ‌œک+کڑœ‌œ ک&JکJک——Jڑ‌ک—Jڑ‌œک—Jڑ‌œکJک—…—ل