/** Turns a List<CubicCurve2D.Float> into a SVG Element representing a sketch of that spline. */
Element splineToSketch(SVGDocument document, List<CubicCurve2D.Float> spline) {
String svgNS = SVGDOMImplementation.SVG_NAMESPACE_URI;
// <g> is an SVG group
// TODO: add a random(ish) rotation to the group
Element group = document.createElementNS(svgNS, "g");
// For each curve in the path, draw along it using a "brush". In
// our case the brush is a simple circle, but this could be changed
// to something more advanced.
for (CubicCurve2D.Float curve : spline) {
// TODO: magic number & step in loop guard
for (double i = 0.0; i <= 1.0; i += 0.01) {
Point2D result = evalParametric(curve, i);
// Add random jitter at some random positive or negative
// distance along the unit normal to the tangent of the
// curve
Point2D n = vectorUnitNormal(evalParametricTangent(curve, i));
float dx = (float) ((Math.random() - 0.5) * n.getX());
float dy = (float) ((Math.random() - 0.5) * n.getY());
Element brush = document.createElementNS(svgNS, "circle");
brush.setAttribute("cx", Double.toString(result.getX() + dx));
brush.setAttribute("cy", Double.toString(result.getY() + dy));
// TODO: magic number for circle radius
brush.setAttribute("r", Double.toString(1.0));
brush.setAttribute("fill", "green");
brush.setAttributeNS(null, "z-index", Integer.toString(zOrder.CONTOUR.ordinal()));
group.appendChild(brush);
}
}
return group;
}
private static Point2D evalParametric(CubicCurve2D curve, double t) {
if (null == curve) {
return null;
}
// B(t) = (1-t)^3 P_0 + 3(1-t)^2t C_1 + 3(1 - t)t^2 C_2 + t^3 P_1
// do nothing fancy, just calculate it.
double rx =
((Math.pow((1 - t), 3) * curve.getX1()))
+ (3 * Math.pow((1 - t), 2) * t * curve.getCtrlX1())
+ (3 * (1 - t) * t * t * curve.getCtrlX2())
+ (t * t * t * curve.getX2());
double ry =
((Math.pow((1 - t), 3) * curve.getY1()))
+ (3 * Math.pow((1 - t), 2) * t * curve.getCtrlY1())
+ (3 * (1 - t) * t * t * curve.getCtrlY2())
+ (t * t * t * curve.getY2());
return new Point2D.Float((float) rx, (float) ry);
}
/**
* Calculates the unit normal of a particular vector, where the vector is represented by the
* direction and magnitude of the line segment from (0,0) to (p.x, p.y).
*
* @param p
* @return
*/
private static Point2D vectorUnitNormal(Point2D p) {
// if null object passed or if the passed vector has zero length
if (null == p || ((0 == p.getX()) && (0 == p.getY()))) {
return null;
}
// normalise the input "vector"
// 1. get length of vector (Pythagoras)
// 2. divide both x and y by this length
// note: c cannot be 0 as we've already considered zero length input
// vectors above.
double c = Math.sqrt((p.getX() * p.getX()) + (p.getY() * p.getY()));
double nvx = p.getX() / c;
double nvy = p.getY() / c;
// Now rotate (nvx, nvy) by 90 degrees to get the normal for the
// input vector.
// rx = nvx * cos (pi/2) - nvy * sin (pi/2)
// ty = nvx * sin (pi/2) + nvy * cos (pi/2)
// but cos (pi/2) = 0 and sin (pi/2) = 1, so this simplifies
return new Point2D.Float((float) (-1 * nvy), (float) nvx);
}