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Consolidate Math aliases.
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@mbostock
mbostock committed Jan 24, 2017
1 parent 3f30a98 commit b17d385
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Showing 2 changed files with 43 additions and 35 deletions.
66 changes: 31 additions & 35 deletions src/arc.js
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
import {path} from "d3-path";
import constant from "./constant";
import {acos, epsilon, pi, halfPi, tau} from "./math";
import {abs, acos, asin, atan2, cos, epsilon, halfPi, max, min, pi, sin, sqrt, tau} from "./math";

function arcInnerRadius(d) {
return d.innerRadius;
Expand All @@ -22,10 +22,6 @@ function arcPadAngle(d) {
return d && d.padAngle; // Note: optional!
}

function asin(x) {
return x >= 1 ? halfPi : x <= -1 ? -halfPi : Math.asin(x);
}

function intersect(x0, y0, x1, y1, x2, y2, x3, y3) {
var x10 = x1 - x0, y10 = y1 - y0,
x32 = x3 - x2, y32 = y3 - y2,
Expand All @@ -38,7 +34,7 @@ function intersect(x0, y0, x1, y1, x2, y2, x3, y3) {
function cornerTangents(x0, y0, x1, y1, r1, rc, cw) {
var x01 = x0 - x1,
y01 = y0 - y1,
lo = (cw ? rc : -rc) / Math.sqrt(x01 * x01 + y01 * y01),
lo = (cw ? rc : -rc) / sqrt(x01 * x01 + y01 * y01),
ox = lo * y01,
oy = -lo * x01,
x11 = x0 + ox,
Expand All @@ -52,7 +48,7 @@ function cornerTangents(x0, y0, x1, y1, r1, rc, cw) {
d2 = dx * dx + dy * dy,
r = r1 - rc,
D = x11 * y10 - x10 * y11,
d = (dy < 0 ? -1 : 1) * Math.sqrt(Math.max(0, r * r * d2 - D * D)),
d = (dy < 0 ? -1 : 1) * sqrt(max(0, r * r * d2 - D * D)),
cx0 = (D * dy - dx * d) / d2,
cy0 = (-D * dx - dy * d) / d2,
cx1 = (D * dy + dx * d) / d2,
Expand Down Expand Up @@ -93,7 +89,7 @@ export default function() {
r1 = +outerRadius.apply(this, arguments),
a0 = startAngle.apply(this, arguments) - halfPi,
a1 = endAngle.apply(this, arguments) - halfPi,
da = Math.abs(a1 - a0),
da = abs(a1 - a0),
cw = a1 > a0;

if (!context) context = buffer = path();
Expand All @@ -106,10 +102,10 @@ export default function() {

// Or is it a circle or annulus?
else if (da > tau - epsilon) {
context.moveTo(r1 * Math.cos(a0), r1 * Math.sin(a0));
context.moveTo(r1 * cos(a0), r1 * sin(a0));
context.arc(0, 0, r1, a0, a1, !cw);
if (r0 > epsilon) {
context.moveTo(r0 * Math.cos(a1), r0 * Math.sin(a1));
context.moveTo(r0 * cos(a1), r0 * sin(a1));
context.arc(0, 0, r0, a1, a0, cw);
}
}
Expand All @@ -123,34 +119,34 @@ export default function() {
da0 = da,
da1 = da,
ap = padAngle.apply(this, arguments) / 2,
rp = (ap > epsilon) && (padRadius ? +padRadius.apply(this, arguments) : Math.sqrt(r0 * r0 + r1 * r1)),
rc = Math.min(Math.abs(r1 - r0) / 2, +cornerRadius.apply(this, arguments)),
rp = (ap > epsilon) && (padRadius ? +padRadius.apply(this, arguments) : sqrt(r0 * r0 + r1 * r1)),
rc = min(abs(r1 - r0) / 2, +cornerRadius.apply(this, arguments)),
rc0 = rc,
rc1 = rc,
t0,
t1;

// Apply padding? Note that since r1 ≥ r0, da1 ≥ da0.
if (rp > epsilon) {
var p0 = asin(rp / r0 * Math.sin(ap)),
p1 = asin(rp / r1 * Math.sin(ap));
var p0 = asin(rp / r0 * sin(ap)),
p1 = asin(rp / r1 * sin(ap));
if ((da0 -= p0 * 2) > epsilon) p0 *= (cw ? 1 : -1), a00 += p0, a10 -= p0;
else da0 = 0, a00 = a10 = (a0 + a1) / 2;
if ((da1 -= p1 * 2) > epsilon) p1 *= (cw ? 1 : -1), a01 += p1, a11 -= p1;
else da1 = 0, a01 = a11 = (a0 + a1) / 2;
}

var x01 = r1 * Math.cos(a01),
y01 = r1 * Math.sin(a01),
x10 = r0 * Math.cos(a10),
y10 = r0 * Math.sin(a10);
var x01 = r1 * cos(a01),
y01 = r1 * sin(a01),
x10 = r0 * cos(a10),
y10 = r0 * sin(a10);

// Apply rounded corners?
if (rc > epsilon) {
var x11 = r1 * Math.cos(a11),
y11 = r1 * Math.sin(a11),
x00 = r0 * Math.cos(a00),
y00 = r0 * Math.sin(a00);
var x11 = r1 * cos(a11),
y11 = r1 * sin(a11),
x00 = r0 * cos(a00),
y00 = r0 * sin(a00);

// Restrict the corner radius according to the sector angle.
if (da < pi) {
Expand All @@ -159,10 +155,10 @@ export default function() {
ay = y01 - oc[1],
bx = x11 - oc[0],
by = y11 - oc[1],
kc = 1 / Math.sin(acos((ax * bx + ay * by) / (Math.sqrt(ax * ax + ay * ay) * Math.sqrt(bx * bx + by * by))) / 2),
lc = Math.sqrt(oc[0] * oc[0] + oc[1] * oc[1]);
rc0 = Math.min(rc, (r0 - lc) / (kc - 1));
rc1 = Math.min(rc, (r1 - lc) / (kc + 1));
kc = 1 / sin(acos((ax * bx + ay * by) / (sqrt(ax * ax + ay * ay) * sqrt(bx * bx + by * by))) / 2),
lc = sqrt(oc[0] * oc[0] + oc[1] * oc[1]);
rc0 = min(rc, (r0 - lc) / (kc - 1));
rc1 = min(rc, (r1 - lc) / (kc + 1));
}
}

Expand All @@ -177,13 +173,13 @@ export default function() {
context.moveTo(t0.cx + t0.x01, t0.cy + t0.y01);

// Have the corners merged?
if (rc1 < rc) context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);
if (rc1 < rc) context.arc(t0.cx, t0.cy, rc1, atan2(t0.y01, t0.x01), atan2(t1.y01, t1.x01), !cw);

// Otherwise, draw the two corners and the ring.
else {
context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
context.arc(0, 0, r1, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
context.arc(t1.cx, t1.cy, rc1, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
context.arc(t0.cx, t0.cy, rc1, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw);
context.arc(0, 0, r1, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
context.arc(t1.cx, t1.cy, rc1, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw);
}
}

Expand All @@ -202,13 +198,13 @@ export default function() {
context.lineTo(t0.cx + t0.x01, t0.cy + t0.y01);

// Have the corners merged?
if (rc0 < rc) context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);
if (rc0 < rc) context.arc(t0.cx, t0.cy, rc0, atan2(t0.y01, t0.x01), atan2(t1.y01, t1.x01), !cw);

// Otherwise, draw the two corners and the ring.
else {
context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
context.arc(0, 0, r0, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw);
context.arc(t1.cx, t1.cy, rc0, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
context.arc(t0.cx, t0.cy, rc0, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw);
context.arc(0, 0, r0, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw);
context.arc(t1.cx, t1.cy, rc0, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw);
}
}

Expand All @@ -224,7 +220,7 @@ export default function() {
arc.centroid = function() {
var r = (+innerRadius.apply(this, arguments) + +outerRadius.apply(this, arguments)) / 2,
a = (+startAngle.apply(this, arguments) + +endAngle.apply(this, arguments)) / 2 - pi / 2;
return [Math.cos(a) * r, Math.sin(a) * r];
return [cos(a) * r, sin(a) * r];
};

arc.innerRadius = function(_) {
Expand Down
12 changes: 12 additions & 0 deletions src/math.js
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Original file line number Diff line number Diff line change
@@ -1,3 +1,11 @@
export var abs = Math.abs;
export var atan2 = Math.atan2;
export var cos = Math.cos;
export var max = Math.max;
export var min = Math.min;
export var sin = Math.sin;
export var sqrt = Math.sqrt;

export var epsilon = 1e-12;
export var pi = Math.PI;
export var halfPi = pi / 2;
Expand All @@ -6,3 +14,7 @@ export var tau = 2 * pi;
export function acos(x) {
return x > 1 ? 0 : x < -1 ? pi : Math.acos(x);
}

export function asin(x) {
return x >= 1 ? halfPi : x <= -1 ? -halfPi : Math.asin(x);
}

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