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zh@YGL`^AAq9^XJi-nZV)v`8E{>me&P0T$9xfv)NpdS^r|j73ob2f$iBp zz{LzI;(p)W?XN9lv-o#$GCT0x-~Oq4HV6D&;?T&%$|a%^umHlCg(lz|1eJiOXjRjM zsRRo+O-5)12`uzPG7BhhK?T`xjev|vD7I;scn%@!oBqc?`p^6@S%Hy7X7Y0eAn abs(ri): + rid = (r1 - r2) / d + if rid > 1: + rid = 1 + if rid < -1: + rid = -1 + beta = asin(rid) + HALF_PI + with pushMatrix(): + translate(p1x, p1y) + angle = atan2(p1x - p2x, p2y - p1y) + rotate(angle + HALF_PI) + x1 = cos(beta) * r1 + y1 = sin(beta) * r1 + x2 = cos(beta) * r2 + y2 = sin(beta) * r2 + #print((d, beta, ri, x1, y1, x2, y2)) + beginShape() + b_arc(0, 0, r1 * 2, r1 * 2, + -beta - PI, beta - PI, mode=2) + b_arc(d, 0, r2 * 2, r2 * 2, + beta - PI, PI - beta, mode=2) + endShape(CLOSE) + + else: + ellipse(p1x, p1y, r1 * 2, r1 * 2) + ellipse(p2x, p2y, r2 * 2, r2 * 2) + +def b_arc(cx, cy, w, h, start_angle, end_angle, mode=0): + """ + A bezier approximation of an arc + using the same signature as the original Processing arc() + mode: 0 "normal" arc, using beginShape() and endShape() + 1 "middle" used in recursive call of smaller arcs + 2 "naked" like normal, but without beginShape() and endShape() + for use inside a larger PShape + """ + theta = end_angle - start_angle + # Compute raw Bezier coordinates. + if mode != 1 or theta < HALF_PI: + x0 = cos(theta / 2.0) + y0 = sin(theta / 2.0) + x3 = x0 + y3 = 0 - y0 + x1 = (4.0 - x0) / 3.0 + if y0 != 0: + y1 = ((1.0 - x0) * (3.0 - x0)) / (3.0 * y0) # y0 != 0... + else: + y1 = 0 + x2 = x1 + y2 = 0 - y1 + # Compute rotationally-offset Bezier coordinates, using: + # x' = cos(angle) * x - sin(angle) * y + # y' = sin(angle) * x + cos(angle) * y + bezAng = start_angle + theta / 2.0 + cBezAng = cos(bezAng) + sBezAng = sin(bezAng) + rx0 = cBezAng * x0 - sBezAng * y0 + ry0 = sBezAng * x0 + cBezAng * y0 + rx1 = cBezAng * x1 - sBezAng * y1 + ry1 = sBezAng * x1 + cBezAng * y1 + rx2 = cBezAng * x2 - sBezAng * y2 + ry2 = sBezAng * x2 + cBezAng * y2 + rx3 = cBezAng * x3 - sBezAng * y3 + ry3 = sBezAng * x3 + cBezAng * y3 + # Compute scaled and translated Bezier coordinates. + rx, ry = w / 2.0, h / 2.0 + px0 = cx + rx * rx0 + py0 = cy + ry * ry0 + px1 = cx + rx * rx1 + py1 = cy + ry * ry1 + px2 = cx + rx * rx2 + py2 = cy + ry * ry2 + px3 = cx + rx * rx3 + py3 = cy + ry * ry3 + # Debug points... comment this out! + # stroke(0) + # ellipse(px3, py3, 15, 15) + # ellipse(px0, py0, 5, 5) + # Drawing + if mode == 0: # 'normal' arc (not 'middle' nor 'naked') + beginShape() + if mode != 1: # if not 'middle' + vertex(px3, py3) + if theta < HALF_PI: + bezierVertex(px2, py2, px1, py1, px0, py0) + else: + # to avoid distortion, break into 2 smaller arcs + b_arc(cx, cy, w, h, start_angle, end_angle - theta / 2.0, mode=1) + b_arc(cx, cy, w, h, start_angle + theta / 2.0, end_angle, mode=1) + if mode == 0: # end of a 'normal' arc + endShape() diff --git a/README.md b/README.md index 9797b4f1..08606e3a 100644 --- a/README.md +++ b/README.md @@ -17,6 +17,11 @@ You may also support my artistic work, open teaching resources and research with --- ## 2019 +--- + +![sketch_190707a](2019/sketch_190707a/sketch_190707a.png) + +[sketch_190707a](https://github.com/villares/sketch-a-day/tree/master/2019/sketch_190707a) [[Py.Processing](https://villares.github.io/como-instalar-o-processing-modo-python/index-EN)] ---