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* Qbezier exact bounding box
* more examples
* Arc convex hull same as exact bounding box (needs to be rotated to fit arc)
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@foo123
foo123 committed Dec 7, 2022
1 parent 6489e9e commit 6109657
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12 changes: 10 additions & 2 deletions README.md
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Expand Up @@ -4,10 +4,18 @@

Computational Geometry and Rendering library for JavaScript

**version: 0.5.0** (74 kB minified)
**version: 0.5.0** (72 kB minified)

Examples:

**Bounding Boxes**

![geometrize bounding boxes](/boundingboxes.png)

**Convex Hulls**

![geometrize convex hulls](/convexhulls.png)

**Intersections**

![geometrize intersections](/intersections.png)
Expand Down Expand Up @@ -40,7 +48,7 @@ intersections.forEach(p => {
});
```

**Shape Tween**
**Shape Tweens**

![geometrize tween between multiple shapes](/shapetween.gif)

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151 changes: 108 additions & 43 deletions build/Geometrize.js
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Expand Up @@ -2,14 +2,14 @@
* Geometrize
* computational geometry and rendering library for JavaScript
*
* @version 0.5.0 (2022-12-07 16:52:30)
* @version 0.5.0 (2022-12-07 20:08:29)
* https://github.com/foo123/Geometrize
*
**//**
* Geometrize
* computational geometry and rendering library for JavaScript
*
* @version 0.5.0 (2022-12-07 16:52:30)
* @version 0.5.0 (2022-12-07 20:08:29)
* https://github.com/foo123/Geometrize
*
**/
Expand Down Expand Up @@ -1001,10 +1001,10 @@ var Primitive = makeClass(null, merge(null, {
return [];
},
getCenter: function() {
var box = this.getBoundingBox();
var bb = this.getBoundingBox();
return {
x: (box.xmin + box.xmax)/2,
y: (box.ymin + box.ymax)/2
x: (bb.xmin + bb.xmax)/2,
y: (bb.ymin + bb.ymax)/2
};
},
hasPoint: function(point) {
Expand Down Expand Up @@ -2454,13 +2454,26 @@ var Arc = makeClass(Curve, {
theta = self.theta,
dtheta = self.dtheta,
theta2 = theta + dtheta,
sweep = self.sweep, otherArc = false,
otherArc = false,
tan = stdMath.tan(rad(self.angle)),
p1, p2, p3, p4, t,
xmin, xmax, ymin, ymax,
txmin, txmax, tymin, tymax
;
// get parameter t by zeroing directional derivatives along x and y
if (!self.sweep)
{
t = theta;
theta = theta2;
theta2 = t;
}
if (theta > theta2)
{
t = theta;
theta = theta2;
theta2 = t;
otherArc = true;
}
// find min/max from zeroes of directional derivative along x and y
// first get of whole ellipse
// along x axis
t = stdMath.atan2(-ry*tan, rx);
Expand Down Expand Up @@ -2507,19 +2520,6 @@ var Arc = makeClass(Curve, {
if (tymin > TWO_PI) tymin -= TWO_PI;
if (tymax < 0) tymax += TWO_PI;
if (tymax > TWO_PI) tymax -= TWO_PI;
if (!self.sweep)
{
t = theta;
theta = theta2;
theta2 = t;
}
if (theta > theta2)
{
t = theta;
theta = theta2;
theta2 = t;
otherArc = true;
}
if ((!otherArc && (theta > txmin || theta2 < txmin)) || (otherArc && !(theta > txmin || theta2 < txmin)))
{
xmin = o1.x < o2.x ? o1 : o2;
Expand Down Expand Up @@ -2552,13 +2552,74 @@ var Arc = makeClass(Curve, {
get: function() {
if (null == _hull)
{
var b = self._bbox;
var bb = self._bbox;
_hull = [
new Point([b.xmin, b.ymin]),
new Point([b.xmax, b.ymin]),
new Point([b.xmax, b.ymax]),
new Point([b.xmin, b.ymax])
new Point([bb.xmin, bb.ymin]),
new Point([bb.xmax, bb.ymin]),
new Point([bb.xmax, bb.ymax]),
new Point([bb.xmin, bb.ymax])
];
/*var c = self.center, rx = self.rX, ry = self.rY,
theta = self.theta, theta2 = theta + self.dtheta,
o1 = self.start, o2 = self.end,
xmin = toarc(-1, 0, c.x, c.y, rx, ry, _cos, _sin),
xmax = toarc(1, 0, c.x, c.y, rx, ry, _cos, _sin),
ymin = toarc(0, -1, c.x, c.y, rx, ry, _cos, _sin),
ymax = toarc(0, 1, c.x, c.y, rx, ry, _cos, _sin),
txmin, txmax, tymin, tymax, t, otherArc = false;
if (!self.sweep)
{
t = theta;
theta = theta2;
theta2 = t;
t = o1;
o1 = o2;
o2 = t;
}
if (theta > theta2)
{
t = theta;
theta = theta2;
theta2 = t;
t = o1;
o1 = o2;
o2 = t;
otherArc = true;
}
txmin = vector_angle(1, 0, xmin.x - c.x, xmin.y - c.y);
txmax = vector_angle(1, 0, xmax.x - c.x, xmax.y - c.y);
tymin = vector_angle(1, 0, ymin.x - c.x, ymin.y - c.y);
tymax = vector_angle(1, 0, ymax.x - c.x, ymax.y - c.y);
if (txmin < 0) txmin += TWO_PI;
if (txmin > TWO_PI) txmin -= TWO_PI;
if (txmax < 0) txmax += TWO_PI;
if (txmax > TWO_PI) txmax -= TWO_PI;
if (tymin < 0) tymin += TWO_PI;
if (tymin > TWO_PI) tymin -= TWO_PI;
if (tymax < 0) tymax += TWO_PI;
if (tymax > TWO_PI) tymax -= TWO_PI;
if ((!otherArc && (theta > txmin || theta2 < txmin)) || (otherArc && !(theta > txmin || theta2 < txmin)))
{
xmin.x = o1.x < o2.x ? o1.x : o2.x;
}
if ((!otherArc && (theta > txmax || theta2 < txmax)) || (otherArc && !(theta > txmax || theta2 < txmax)))
{
xmax.x = o1.x > o2.x ? o1.x : o2.x;
}
if ((!otherArc && (theta > tymin || theta2 < tymin)) || (otherArc && !(theta > tymin || theta2 < tymin)))
{
ymin.y = o1.y < o2.y ? o1.y : o2.y;
}
if ((!otherArc && (theta > tymax || theta2 < tymax)) || (otherArc && !(theta > tymax || theta2 < tymax)))
{
ymax.y = o1.y > o2.y ? o1.y : o2.y;
}
_hull = [
new Point(xmin.x, ymin.y),
new Point(xmax.x, ymin.y),
new Point(xmax.x, ymax.y),
new Point(xmin.x, ymax.y)
];*/
}
return _hull;
},
Expand Down Expand Up @@ -2738,12 +2799,16 @@ var Bezier2 = makeClass(Bezier, {
get: function() {
if (null == _bbox)
{
// find min/max from zeroes of directional derivative along x and y
var p = self._points,
p1 = p[0], p2 = p[1], p3 = p[2],
xmin = stdMath.min(p1.x, p2.x, p3.x),
xmax = stdMath.max(p1.x, p2.x, p3.x),
ymin = stdMath.min(p1.y, p2.y, p3.y),
ymax = stdMath.max(p1.y, p2.y, p3.y)
ax = p[0].x - 2*p[1].x + p[2].x,
px = is_strictly_equal(ax, 0) ? p[1] : self.f((p[0].x - p[1].x)/ax),
ay = p[0].y - 2*p[1].y + p[2].y,
py = is_strictly_equal(ay, 0) ? p[1] : self.f((p[0].y - p[1].y)/ay),
xmin = stdMath.min(px.x, p[0].x, p[2].x),
xmax = stdMath.max(px.x, p[0].x, p[2].x),
ymin = stdMath.min(py.y, p[0].y, p[2].y),
ymax = stdMath.max(py.y, p[0].y, p[2].y)
;
_bbox = {
ymin: ymin,
Expand Down Expand Up @@ -3507,7 +3572,7 @@ var Ellipse = makeClass(Curve, {
tan = stdMath.tan(rad(self.angle)),
p1, p2, p3, p4, t
;
// get parameter t by zeroing directional derivatives along x and y
// find min/max from zeroes of directional derivative along x and y
// along x axis
t = stdMath.atan2(-ry*tan, rx);
p1 = arc(t, c.x, c.y, rx, ry, _cos, _sin);
Expand Down Expand Up @@ -4411,12 +4476,12 @@ function point_on_qbezier(p, c)
{
//x = t^{2} \left(x_{1} - 2 x_{2} + x_{3}\right) + t \left(- 2 x_{1} + 2 x_{2}\right) + x_{1}
var tx, ty;
tx = quad_solve(c[0].x - 2*c[1].x + c[2].x, -2*c[0].x + 2*c[1].x, c[0].x - p.x);
tx = solve_quadratic(c[0].x - 2*c[1].x + c[2].x, -2*c[0].x + 2*c[1].x, c[0].x - p.x);
if (!tx) return false;
if (1 < tx.length && (0 > tx[1] || 1 < tx[1])) tx.pop();
if (tx.length && (0 > tx[0] || 1 < tx[0])) tx.shift();
if (!tx.length) return false;
ty = quad_solve(c[0].y - 2*c[1].y + c[2].y, -2*c[0].y + 2*c[1].y, c[0].y - p.y);
ty = solve_quadratic(c[0].y - 2*c[1].y + c[2].y, -2*c[0].y + 2*c[1].y, c[0].y - p.y);
if (!ty) return false;
if (1 < ty.length && (0 > ty[1] || 1 < ty[1])) ty.pop();
if (ty.length && (0 > ty[0] || 1 < ty[0])) ty.shift();
Expand Down Expand Up @@ -4796,22 +4861,22 @@ function is_convex(points)
}
return 1 === abs(stdMath.round(angle_sum / TWO_PI));
}
function lin_solve(a, b)
function solve_linear(a, b)
{
return is_strictly_equal(a, 0) ? false : [-b/a];
}
function quad_solve(a, b, c)
function solve_quadratic(a, b, c)
{
if (is_strictly_equal(a, 0)) return lin_solve(b, c);
if (is_strictly_equal(a, 0)) return solve_linear(b, c);
var D = b*b - 4*a*c, DS = 0;
if (is_almost_equal(D, 0)) return [-b/(2*a)];
if (0 > D) return false;
DS = sqrt(D);
return [(-b-DS)/(2*a), (-b+DS)/(2*a)];
}
function cub_solve(a, b, c, d)
function solve_cubic(a, b, c, d)
{
if (is_strictly_equal(a, 0)) return quad_solve(b, c, d);
if (is_strictly_equal(a, 0)) return solve_quadratic(b, c, d);
var A = b/a, B = c/a, C = d/a,
Q = (3*B - A*A)/9, QS = 0,
R = (9*A*B - 27*C - 2*pow(A, 3))/54,
Expand Down Expand Up @@ -4869,10 +4934,10 @@ function line_quadratic_intersection(m, n, k, a, b, c, d, e, f)
var x, y, x1 = 0, y1 = 0, x2 = 0, y2 = 0, D = 0, R = 0, F = 0;
if (is_strictly_equal(m, 0))
{
y = lin_solve(n, k);
y = solve_linear(n, k);
if (!y) return false;
y1 = y[0];
x = quad_solve(a, c*y1+d, b*y1*y1+e*y1+f);
x = solve_quadratic(a, c*y1+d, b*y1*y1+e*y1+f);
if (!x) return false;
return 2 === x.length ? [{x:x[0],y:y1},{x:x[1],y:y1}] : [{x:x[0],y:y1}];
}
Expand Down Expand Up @@ -5499,9 +5564,9 @@ function is_function(x)
Geometrize.Math.deg = deg;
Geometrize.Math.rad = rad;
Geometrize.Math.hypot = hypot;
Geometrize.Math.solve1 = lin_solve;
Geometrize.Math.solve2 = quad_solve;
Geometrize.Math.solve3 = cub_solve;
Geometrize.Math.solveLinear = solve_linear;
Geometrize.Math.solveQuadratic = solve_quadratic;
Geometrize.Math.solveCubic = solve_cubic;

// export it
return Geometrize;
Expand Down
5 changes: 3 additions & 2 deletions build/Geometrize.min.js
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