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/*
* Copyright (c) 2018-2019. data2viz sàrl.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*/
package io.data2viz.shape
import io.data2viz.geom.Path
import kotlin.math.*
/**
* Instanciate a new ArcBuilder and use the lambda to initiate it.
*/
fun arcBuilder(init: ArcBuilder.() -> Unit) = ArcBuilder().apply(init)
/**
*
*/
class ArcBuilder {
var innerRadius: (D) -> Double = const(.0)
var outerRadius: (D) -> Double = const(100.0)
var cornerRadius: (D) -> Double = const(.0)
var padRadius: ((D) -> Double)? = null
var startAngle: (D) -> Double = const(.0) // TODO : Angle ?
var endAngle: (D) -> Double = const(.0) // TODO : Angle ?
var padAngle: (D) -> Double = const(.0) // TODO : Angle ?
fun centroid(datum: D): Array {
val r = innerRadius(datum) + outerRadius(datum) / 2.0
val a = startAngle(datum) + endAngle(datum) / 2.0 - halfPi
return arrayOf(cos(a) * r, sin(a) * r)
}
/**
* Use the datum to generate an arc on the path
*/
fun buildArcForDatum(datum: D, path: C): C {
var r0 = innerRadius(datum)
var r1 = outerRadius(datum)
val a0 = startAngle(datum) - halfPi
val a1 = endAngle(datum) - halfPi
val da = abs(a1 - a0)
val cw = a1 > a0
// Ensure that the outer radius is always larger than the inner radius.
if (r1 < r0) {
val r = r1
r1 = r0
r0 = r
}
// Is it a point?
if (r1 <= epsilon) path.moveTo(0.0, 0.0)
// Or is it a circle or annulus?
else if (da > tau - epsilon) {
path.moveTo(r1 * cos(a0), r1 * sin(a0));
path.arc(.0, .0, r1, a0, a1, !cw);
if (r0 > epsilon) {
path.moveTo(r0 * cos(a1), r0 * sin(a1));
path.arc(.0, .0, r0, a1, a0, cw);
}
}
// Or is it a circular or annular sector?
else {
var a01 = a0
var a11 = a1
var a00 = a0
var a10 = a1
var da0 = da
var da1 = da
val ap = padAngle(datum) / 2.0
val rp = if (ap <= epsilon) 0.0 else {
val temp = if (padRadius != null) padRadius!!(datum) else sqrt(r0 * r0 + r1 * r1)
if (temp != 0.0) 1.0 else 0.0
}
val rc = min(abs(r1 - r0) / 2, cornerRadius(datum))
var rc0 = rc
var rc1 = rc
// Apply padding? Note that since r1 ≥ r0, da1 ≥ da0.
if (rp > epsilon) {
var p0 = asin(rp / r0 * ap)
var p1 = asin(rp / r1 * ap)
da0 -= p0 * 2
if (da0 > epsilon) {
p0 *= if (cw) 1.0 else -1.0
a00 += p0
a10 -= p0
} else {
da0 = .0
a10 = (a0 + a1) / 2
a00 = a10
}
da1 -= p1 * 2
if (da1 > epsilon) {
p1 *= if (cw) 1.0 else -1.0
a01 += p1
a11 -= p1
} else {
da1 = .0
a11 = (a0 + a1) / 2
a01 = a11
}
}
val x01 = r1 * cos(a01)
val y01 = r1 * sin(a01)
val x10 = r0 * cos(a10)
val y10 = r0 * sin(a10)
val x11 = r1 * cos(a11)
val y11 = r1 * sin(a11)
val x00 = r0 * cos(a00)
val y00 = r0 * sin(a00)
// Apply rounded corners?
if (rc > epsilon) {
// Restrict the corner radius according to the sector angle.
if (da < pi) {
val oc = if (da0 > epsilon) intersect(x01, y01, x00, y00, x11, y11, x10, y10) else arrayOf(x10, y10)
val ax = x01 - oc[0]
val ay = y01 - oc[1]
val bx = x11 - oc[0]
val by = y11 - oc[1]
val kc = 1 / sin(acos((ax * bx + ay * by) / (sqrt(ax * ax + ay * ay) * sqrt(bx * bx + by * by))) / 2)
val lc = sqrt(oc[0] * oc[0] + oc[1] * oc[1])
rc0 = min(rc, (r0 - lc) / (kc - 1))
rc1 = min(rc, (r1 - lc) / (kc + 1))
}
}
// Is the sector collapsed to a line?
if (!(da1 > epsilon)) path.moveTo(x01, y01)
// Does the sector’s outer ring have rounded corners?
else if (rc1 > epsilon) {
val t0 = cornerTangents(x00, y00, x01, y01, r1, rc1, cw);
val t1 = cornerTangents(x11, y11, x10, y10, r1, rc1, cw);
path.moveTo(t0.cx + t0.x01, t0.cy + t0.y01);
// Have the corners merged?
if (rc1 < rc) path.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 {
path.arc(t0.cx, t0.cy, rc1, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw);
path.arc(.0, .0, r1, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
path.arc(t1.cx, t1.cy, rc1, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw);
}
}
// Or is the outer ring just a circular arc?
else {
path.moveTo(x01, y01)
path.arc(.0, .0, r1, a01, a11, !cw)
}
// Is there no inner ring, and it’s a circular sector?
// Or perhaps it’s an annular sector collapsed due to padding?
if (!(r0 > epsilon) || !(da0 > epsilon)) path.lineTo(x10, y10)
// Does the sector’s inner ring (or point) have rounded corners?
else if (rc0 > epsilon) {
val t0 = cornerTangents(x10, y10, x11, y11, r0, -rc0, cw)
val t1 = cornerTangents(x01, y01, x00, y00, r0, -rc0, cw)
path.lineTo(t0.cx + t0.x01, t0.cy + t0.y01)
// Have the corners merged?
if (rc0 < rc) path.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 {
path.arc(t0.cx, t0.cy, rc0, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw)
path.arc(.0, .0, r0, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw)
path.arc(t1.cx, t1.cy, rc0, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw)
}
}
// Or is the inner ring just a circular arc?
else path.arc(.0, .0, r0, a10, a00, cw);
}
path.closePath();
return path
}
// Compute perpendicular offset line of length rc.
// http://mathworld.wolfram.com/Circle-LineIntersection.html
private fun cornerTangents(x0: Double, y0: Double, x1: Double, y1: Double, r1: Double, rc: Double, cw: Boolean): CornerTangentValues {
val x01 = x0 - x1
val y01 = y0 - y1
val lo = (if (cw) rc else -rc) / sqrt(x01 * x01 + y01 * y01)
val ox = lo * y01
val oy = -lo * x01
val x11 = x0 + ox
val y11 = y0 + oy
val x10 = x1 + ox
val y10 = y1 + oy
val x00 = (x11 + x10) / 2
val y00 = (y11 + y10) / 2
val dx = x10 - x11
val dy = y10 - y11
val d2 = dx * dx + dy * dy
val r = r1 - rc
val D = x11 * y10 - x10 * y11
val d = (if (dy < 0) -1.0 else 1.0) * sqrt(max(.0, r * r * d2 - D * D))
var cx0 = (D * dy - dx * d) / d2
var cy0 = (-D * dx - dy * d) / d2
val cx1 = (D * dy + dx * d) / d2
val cy1 = (-D * dx + dy * d) / d2
val dx0 = cx0 - x00
val dy0 = cy0 - y00
val dx1 = cx1 - x00
val dy1 = cy1 - y00
// Pick the closer of the two intersection points.
if (dx0 * dx0 + dy0 * dy0 > dx1 * dx1 + dy1 * dy1) {
cx0 = cx1
cy0 = cy1
}
return CornerTangentValues(cx0, cy0, -ox, -oy, cx0 * (r1 / r - 1), cy0 * (r1 / r - 1))
}
private fun intersect(x0: Double, y0: Double, x1: Double, y1: Double, x2: Double, y2: Double, x3: Double, y3: Double): Array {
val x10 = x1 - x0
val y10 = y1 - y0
val x32 = x3 - x2
val y32 = y3 - y2
val t = (x32 * (y0 - y2) - y32 * (x0 - x2)) / (y32 * x10 - x32 * y10)
return arrayOf(x0 + t * x10, y0 + t * y10)
}
}
data class ArcParams(
val startAngle: Double,
val endAngle: Double,
val padAngle: Double?,
val value: Double?,
val index: Int?,
val data: T?
)
private data class CornerTangentValues(
val cx: Double,
val cy: Double,
val x01: Double,
val y01: Double,
val x11: Double,
val y11: Double
)
