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components/sections/tightbounds/index.js

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+var React = require("react");
+var Graphic = require("../../Graphic.jsx");
+var SectionHeader = require("../../SectionHeader.jsx");
+
+var TightBounds = React.createClass({
+  getDefaultProps: function() {
+    return {
+      title: "Tight boxes"
+    };
+  },
+
+  setupQuadratic: function(api) {
+    var curve = api.getDefaultQuadratic();
+    api.setCurve(curve);
+  },
+
+  setupCubic: function(api) {
+    var curve = api.getDefaultCubic();
+    api.setCurve(curve);
+  },
+
+  align: function(points, line) {
+    var tx = line.p1.x,
+        ty = line.p1.y,
+        a = -Math.atan2(line.p2.y-ty, line.p2.x-tx),
+        cos = Math.cos,
+        sin = Math.sin,
+        d = function(v) {
+          return {
+            x: (v.x-tx)*cos(a) - (v.y-ty)*sin(a),
+            y: (v.x-tx)*sin(a) + (v.y-ty)*cos(a),
+            a: a
+          };
+        };
+    return points.map(d);
+  },
+
+  // FIXME: I'm not satisfied with needing to turn a bbox[] into a point[],
+  //        this needs a bezier.js solution, really, with a  call curve.tightbbox()
+  transpose: function(points, angle, offset) {
+    var tx = offset.x,
+        ty = offset.y,
+        cos = Math.cos,
+        sin = Math.sin,
+        v = [points.x.min, points.y.min, points.x.max, points.y.max],
+        points = [
+          {x: v[0], y: v[1] },
+          {x: v[2], y: v[1] },
+          {x: v[2], y: v[3] },
+          {x: v[0], y: v[3] }
+        ].map(p => {
+          var x=p.x, y=p.y;
+          return {
+            x: x*cos(angle) - y*sin(angle) + tx,
+            y: x*sin(angle) + y*cos(angle) + ty
+          };
+        });
+    return points;
+  },
+
+  draw: function(api, curve) {
+    api.reset();
+    api.drawSkeleton(curve);
+    api.drawCurve(curve);
+
+    var pts = curve.points;
+    var line = {p1: pts[0], p2: pts[pts.length-1]};
+    var apts = this.align(pts, line);
+    var angle = -apts[0].a;
+    var aligned = new api.Bezier(apts);
+    var bbox = aligned.bbox();
+    var tpts = this.transpose(bbox, angle, pts[0]);
+
+    api.setColor("#00FF00");
+    api.drawLine(tpts[0], tpts[1]);
+    api.drawLine(tpts[1], tpts[2]);
+    api.drawLine(tpts[2], tpts[3]);
+    api.drawLine(tpts[3], tpts[0]);
+  },
+
+  render: function() {
+    return (
+      <section>
+        <SectionHeader {...this.props} />
+
+        <p>With our knowledge of bounding boxes, and curve alignment, We can now form the "tight" bounding box for
+        curves. We first align  our curve, recording the translation we performed, "T", and the rotation angle we
+        used, "R". We then determine the aligned curve's normal bounding box. Once we have that, we can map that
+        bounding box back to our original curve by rotating it by -R, and then translating it by -T. We now have
+        nice tight bounding boxes for our curves:</p>
+
+        <Graphic preset="twopanel" title="Aligning a quadratic curve" setup={this.setupQuadratic} draw={this.draw} />
+        <Graphic preset="twopanel" title="Aligning a cubic curve" setup={this.setupCubic} draw={this.draw} />
+
+        <p>These are, strictly speaking, not necessarily the tightest possible bounding boxes. It is possible to compute
+        the optimal bounding box by determining which spanning lines we need to effect a minimal box area, but because
+        of the parametric nature of Bézier curves this is actually a rather costly operation, and the gain in bounding
+        precision is often not worth it. If there is high demand for it, I'll add a section on how to precisely compute
+        the best fit bounding box, but the maths is fairly gruelling and just not really worth spending time on.</p>
+
+      </section>
+    );
+  }
+});
+
+module.exports = TightBounds;