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matterbridge/vendor/github.com/Benau/go_rlottie/vector_vpath.cpp

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/*
* Copyright (c) 2020 Samsung Electronics Co., Ltd. All rights reserved.
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "vector_vpath.h"
#include <cassert>
#include <iterator>
#include <vector>
#include "vector_vbezier.h"
#include "vector_vdebug.h"
#include "vector_vline.h"
#include "vector_vrect.h"
V_BEGIN_NAMESPACE
void VPath::VPathData::transform(const VMatrix &m)
{
for (auto &i : m_points) {
i = m.map(i);
}
mLengthDirty = true;
}
float VPath::VPathData::length() const
{
if (!mLengthDirty) return mLength;
mLengthDirty = false;
mLength = 0.0;
size_t i = 0;
for (auto e : m_elements) {
switch (e) {
case VPath::Element::MoveTo:
i++;
break;
case VPath::Element::LineTo: {
mLength += VLine(m_points[i - 1], m_points[i]).length();
i++;
break;
}
case VPath::Element::CubicTo: {
mLength += VBezier::fromPoints(m_points[i - 1], m_points[i],
m_points[i + 1], m_points[i + 2])
.length();
i += 3;
break;
}
case VPath::Element::Close:
break;
}
}
return mLength;
}
void VPath::VPathData::checkNewSegment()
{
if (mNewSegment) {
moveTo(0, 0);
mNewSegment = false;
}
}
void VPath::VPathData::moveTo(float x, float y)
{
mStartPoint = {x, y};
mNewSegment = false;
m_elements.emplace_back(VPath::Element::MoveTo);
m_points.emplace_back(x, y);
m_segments++;
mLengthDirty = true;
}
void VPath::VPathData::lineTo(float x, float y)
{
checkNewSegment();
m_elements.emplace_back(VPath::Element::LineTo);
m_points.emplace_back(x, y);
mLengthDirty = true;
}
void VPath::VPathData::cubicTo(float cx1, float cy1, float cx2, float cy2,
float ex, float ey)
{
checkNewSegment();
m_elements.emplace_back(VPath::Element::CubicTo);
m_points.emplace_back(cx1, cy1);
m_points.emplace_back(cx2, cy2);
m_points.emplace_back(ex, ey);
mLengthDirty = true;
}
void VPath::VPathData::close()
{
if (empty()) return;
const VPointF &lastPt = m_points.back();
if (!fuzzyCompare(mStartPoint, lastPt)) {
lineTo(mStartPoint.x(), mStartPoint.y());
}
m_elements.push_back(VPath::Element::Close);
mNewSegment = true;
mLengthDirty = true;
}
void VPath::VPathData::reset()
{
if (empty()) return;
m_elements.clear();
m_points.clear();
m_segments = 0;
mLength = 0;
mLengthDirty = false;
}
size_t VPath::VPathData::segments() const
{
return m_segments;
}
void VPath::VPathData::reserve(size_t pts, size_t elms)
{
if (m_points.capacity() < m_points.size() + pts)
m_points.reserve(m_points.size() + pts);
if (m_elements.capacity() < m_elements.size() + elms)
m_elements.reserve(m_elements.size() + elms);
}
static VPointF curvesForArc(const VRectF &, float, float, VPointF *, size_t *);
static constexpr float PATH_KAPPA = 0.5522847498f;
static constexpr float K_PI = 3.141592f;
void VPath::VPathData::arcTo(const VRectF &rect, float startAngle,
float sweepLength, bool forceMoveTo)
{
size_t point_count = 0;
VPointF pts[15];
VPointF curve_start =
curvesForArc(rect, startAngle, sweepLength, pts, &point_count);
reserve(point_count + 1, point_count / 3 + 1);
if (empty() || forceMoveTo) {
moveTo(curve_start.x(), curve_start.y());
} else {
lineTo(curve_start.x(), curve_start.y());
}
for (size_t i = 0; i < point_count; i += 3) {
cubicTo(pts[i].x(), pts[i].y(), pts[i + 1].x(), pts[i + 1].y(),
pts[i + 2].x(), pts[i + 2].y());
}
}
void VPath::VPathData::addCircle(float cx, float cy, float radius,
VPath::Direction dir)
{
addOval(VRectF(cx - radius, cy - radius, 2 * radius, 2 * radius), dir);
}
void VPath::VPathData::addOval(const VRectF &rect, VPath::Direction dir)
{
if (rect.empty()) return;
float x = rect.x();
float y = rect.y();
float w = rect.width();
float w2 = rect.width() / 2;
float w2k = w2 * PATH_KAPPA;
float h = rect.height();
float h2 = rect.height() / 2;
float h2k = h2 * PATH_KAPPA;
reserve(13, 6); // 1Move + 4Cubic + 1Close
if (dir == VPath::Direction::CW) {
// moveto 12 o'clock.
moveTo(x + w2, y);
// 12 -> 3 o'clock
cubicTo(x + w2 + w2k, y, x + w, y + h2 - h2k, x + w, y + h2);
// 3 -> 6 o'clock
cubicTo(x + w, y + h2 + h2k, x + w2 + w2k, y + h, x + w2, y + h);
// 6 -> 9 o'clock
cubicTo(x + w2 - w2k, y + h, x, y + h2 + h2k, x, y + h2);
// 9 -> 12 o'clock
cubicTo(x, y + h2 - h2k, x + w2 - w2k, y, x + w2, y);
} else {
// moveto 12 o'clock.
moveTo(x + w2, y);
// 12 -> 9 o'clock
cubicTo(x + w2 - w2k, y, x, y + h2 - h2k, x, y + h2);
// 9 -> 6 o'clock
cubicTo(x, y + h2 + h2k, x + w2 - w2k, y + h, x + w2, y + h);
// 6 -> 3 o'clock
cubicTo(x + w2 + w2k, y + h, x + w, y + h2 + h2k, x + w, y + h2);
// 3 -> 12 o'clock
cubicTo(x + w, y + h2 - h2k, x + w2 + w2k, y, x + w2, y);
}
close();
}
void VPath::VPathData::addRect(const VRectF &rect, VPath::Direction dir)
{
float x = rect.x();
float y = rect.y();
float w = rect.width();
float h = rect.height();
if (vCompare(w, 0.f) && vCompare(h, 0.f)) return;
reserve(5, 6); // 1Move + 4Line + 1Close
if (dir == VPath::Direction::CW) {
moveTo(x + w, y);
lineTo(x + w, y + h);
lineTo(x, y + h);
lineTo(x, y);
close();
} else {
moveTo(x + w, y);
lineTo(x, y);
lineTo(x, y + h);
lineTo(x + w, y + h);
close();
}
}
void VPath::VPathData::addRoundRect(const VRectF &rect, float roundness,
VPath::Direction dir)
{
if (2 * roundness > rect.width()) roundness = rect.width() / 2.0f;
if (2 * roundness > rect.height()) roundness = rect.height() / 2.0f;
addRoundRect(rect, roundness, roundness, dir);
}
void VPath::VPathData::addRoundRect(const VRectF &rect, float rx, float ry,
VPath::Direction dir)
{
if (vCompare(rx, 0.f) || vCompare(ry, 0.f)) {
addRect(rect, dir);
return;
}
float x = rect.x();
float y = rect.y();
float w = rect.width();
float h = rect.height();
// clamp the rx and ry radius value.
rx = 2 * rx;
ry = 2 * ry;
if (rx > w) rx = w;
if (ry > h) ry = h;
reserve(17, 10); // 1Move + 4Cubic + 1Close
if (dir == VPath::Direction::CW) {
moveTo(x + w, y + ry / 2.f);
arcTo(VRectF(x + w - rx, y + h - ry, rx, ry), 0, -90, false);
arcTo(VRectF(x, y + h - ry, rx, ry), -90, -90, false);
arcTo(VRectF(x, y, rx, ry), -180, -90, false);
arcTo(VRectF(x + w - rx, y, rx, ry), -270, -90, false);
close();
} else {
moveTo(x + w, y + ry / 2.f);
arcTo(VRectF(x + w - rx, y, rx, ry), 0, 90, false);
arcTo(VRectF(x, y, rx, ry), 90, 90, false);
arcTo(VRectF(x, y + h - ry, rx, ry), 180, 90, false);
arcTo(VRectF(x + w - rx, y + h - ry, rx, ry), 270, 90, false);
close();
}
}
static float tForArcAngle(float angle);
void findEllipseCoords(const VRectF &r, float angle, float length,
VPointF *startPoint, VPointF *endPoint)
{
if (r.empty()) {
if (startPoint) *startPoint = VPointF();
if (endPoint) *endPoint = VPointF();
return;
}
float w2 = r.width() / 2;
float h2 = r.height() / 2;
float angles[2] = {angle, angle + length};
VPointF *points[2] = {startPoint, endPoint};
for (int i = 0; i < 2; ++i) {
if (!points[i]) continue;
float theta = angles[i] - 360 * floorf(angles[i] / 360);
float t = theta / 90;
// truncate
int quadrant = int(t);
t -= quadrant;
t = tForArcAngle(90 * t);
// swap x and y?
if (quadrant & 1) t = 1 - t;
float a, b, c, d;
VBezier::coefficients(t, a, b, c, d);
VPointF p(a + b + c * PATH_KAPPA, d + c + b * PATH_KAPPA);
// left quadrants
if (quadrant == 1 || quadrant == 2) p.rx() = -p.x();
// top quadrants
if (quadrant == 0 || quadrant == 1) p.ry() = -p.y();
*points[i] = r.center() + VPointF(w2 * p.x(), h2 * p.y());
}
}
static float tForArcAngle(float angle)
{
float radians, cos_angle, sin_angle, tc, ts, t;
if (vCompare(angle, 0.f)) return 0;
if (vCompare(angle, 90.0f)) return 1;
radians = (angle / 180) * K_PI;
cos_angle = cosf(radians);
sin_angle = sinf(radians);
// initial guess
tc = angle / 90;
// do some iterations of newton's method to approximate cos_angle
// finds the zero of the function b.pointAt(tc).x() - cos_angle
tc -= ((((2 - 3 * PATH_KAPPA) * tc + 3 * (PATH_KAPPA - 1)) * tc) * tc + 1 -
cos_angle) // value
/ (((6 - 9 * PATH_KAPPA) * tc + 6 * (PATH_KAPPA - 1)) *
tc); // derivative
tc -= ((((2 - 3 * PATH_KAPPA) * tc + 3 * (PATH_KAPPA - 1)) * tc) * tc + 1 -
cos_angle) // value
/ (((6 - 9 * PATH_KAPPA) * tc + 6 * (PATH_KAPPA - 1)) *
tc); // derivative
// initial guess
ts = tc;
// do some iterations of newton's method to approximate sin_angle
// finds the zero of the function b.pointAt(tc).y() - sin_angle
ts -= ((((3 * PATH_KAPPA - 2) * ts - 6 * PATH_KAPPA + 3) * ts +
3 * PATH_KAPPA) *
ts -
sin_angle) /
(((9 * PATH_KAPPA - 6) * ts + 12 * PATH_KAPPA - 6) * ts +
3 * PATH_KAPPA);
ts -= ((((3 * PATH_KAPPA - 2) * ts - 6 * PATH_KAPPA + 3) * ts +
3 * PATH_KAPPA) *
ts -
sin_angle) /
(((9 * PATH_KAPPA - 6) * ts + 12 * PATH_KAPPA - 6) * ts +
3 * PATH_KAPPA);
// use the average of the t that best approximates cos_angle
// and the t that best approximates sin_angle
t = 0.5f * (tc + ts);
return t;
}
// The return value is the starting point of the arc
static VPointF curvesForArc(const VRectF &rect, float startAngle,
float sweepLength, VPointF *curves,
size_t *point_count)
{
if (rect.empty()) {
return {};
}
float x = rect.x();
float y = rect.y();
float w = rect.width();
float w2 = rect.width() / 2;
float w2k = w2 * PATH_KAPPA;
float h = rect.height();
float h2 = rect.height() / 2;
float h2k = h2 * PATH_KAPPA;
VPointF points[16] = {
// start point
VPointF(x + w, y + h2),
// 0 -> 270 degrees
VPointF(x + w, y + h2 + h2k), VPointF(x + w2 + w2k, y + h),
VPointF(x + w2, y + h),
// 270 -> 180 degrees
VPointF(x + w2 - w2k, y + h), VPointF(x, y + h2 + h2k),
VPointF(x, y + h2),
// 180 -> 90 degrees
VPointF(x, y + h2 - h2k), VPointF(x + w2 - w2k, y), VPointF(x + w2, y),
// 90 -> 0 degrees
VPointF(x + w2 + w2k, y), VPointF(x + w, y + h2 - h2k),
VPointF(x + w, y + h2)};
if (sweepLength > 360)
sweepLength = 360;
else if (sweepLength < -360)
sweepLength = -360;
// Special case fast paths
if (startAngle == 0.0f) {
if (vCompare(sweepLength, 360)) {
for (int i = 11; i >= 0; --i) curves[(*point_count)++] = points[i];
return points[12];
} else if (vCompare(sweepLength, -360)) {
for (int i = 1; i <= 12; ++i) curves[(*point_count)++] = points[i];
return points[0];
}
}
int startSegment = int(floorf(startAngle / 90.0f));
int endSegment = int(floorf((startAngle + sweepLength) / 90.0f));
float startT = (startAngle - startSegment * 90) / 90;
float endT = (startAngle + sweepLength - endSegment * 90) / 90;
int delta = sweepLength > 0 ? 1 : -1;
if (delta < 0) {
startT = 1 - startT;
endT = 1 - endT;
}
// avoid empty start segment
if (vIsZero(startT - float(1))) {
startT = 0;
startSegment += delta;
}
// avoid empty end segment
if (vIsZero(endT)) {
endT = 1;
endSegment -= delta;
}
startT = tForArcAngle(startT * 90);
endT = tForArcAngle(endT * 90);
const bool splitAtStart = !vIsZero(startT);
const bool splitAtEnd = !vIsZero(endT - float(1));
const int end = endSegment + delta;
// empty arc?
if (startSegment == end) {
const int quadrant = 3 - ((startSegment % 4) + 4) % 4;
const int j = 3 * quadrant;
return delta > 0 ? points[j + 3] : points[j];
}
VPointF startPoint, endPoint;
findEllipseCoords(rect, startAngle, sweepLength, &startPoint, &endPoint);
for (int i = startSegment; i != end; i += delta) {
const int quadrant = 3 - ((i % 4) + 4) % 4;
const int j = 3 * quadrant;
VBezier b;
if (delta > 0)
b = VBezier::fromPoints(points[j + 3], points[j + 2], points[j + 1],
points[j]);
else
b = VBezier::fromPoints(points[j], points[j + 1], points[j + 2],
points[j + 3]);
// empty arc?
if (startSegment == endSegment && vCompare(startT, endT))
return startPoint;
if (i == startSegment) {
if (i == endSegment && splitAtEnd)
b = b.onInterval(startT, endT);
else if (splitAtStart)
b = b.onInterval(startT, 1);
} else if (i == endSegment && splitAtEnd) {
b = b.onInterval(0, endT);
}
// push control points
curves[(*point_count)++] = b.pt2();
curves[(*point_count)++] = b.pt3();
curves[(*point_count)++] = b.pt4();
}
curves[*(point_count)-1] = endPoint;
return startPoint;
}
void VPath::VPathData::addPolystar(float points, float innerRadius,
float outerRadius, float innerRoundness,
float outerRoundness, float startAngle,
float cx, float cy, VPath::Direction dir)
{
const static float POLYSTAR_MAGIC_NUMBER = 0.47829f / 0.28f;
float currentAngle = (startAngle - 90.0f) * K_PI / 180.0f;
float x;
float y;
float partialPointRadius = 0;
float anglePerPoint = (2.0f * K_PI / points);
float halfAnglePerPoint = anglePerPoint / 2.0f;
float partialPointAmount = points - floorf(points);
bool longSegment = false;
size_t numPoints = size_t(ceilf(points) * 2);
float angleDir = ((dir == VPath::Direction::CW) ? 1.0f : -1.0f);
bool hasRoundness = false;
innerRoundness /= 100.0f;
outerRoundness /= 100.0f;
if (!vCompare(partialPointAmount, 0)) {
currentAngle +=
halfAnglePerPoint * (1.0f - partialPointAmount) * angleDir;
}
if (!vCompare(partialPointAmount, 0)) {
partialPointRadius =
innerRadius + partialPointAmount * (outerRadius - innerRadius);
x = partialPointRadius * cosf(currentAngle);
y = partialPointRadius * sinf(currentAngle);
currentAngle += anglePerPoint * partialPointAmount / 2.0f * angleDir;
} else {
x = outerRadius * cosf(currentAngle);
y = outerRadius * sinf(currentAngle);
currentAngle += halfAnglePerPoint * angleDir;
}
if (vIsZero(innerRoundness) && vIsZero(outerRoundness)) {
reserve(numPoints + 2, numPoints + 3);
} else {
reserve(numPoints * 3 + 2, numPoints + 3);
hasRoundness = true;
}
moveTo(x + cx, y + cy);
for (size_t i = 0; i < numPoints; i++) {
float radius = longSegment ? outerRadius : innerRadius;
float dTheta = halfAnglePerPoint;
if (!vIsZero(partialPointRadius) && i == numPoints - 2) {
dTheta = anglePerPoint * partialPointAmount / 2.0f;
}
if (!vIsZero(partialPointRadius) && i == numPoints - 1) {
radius = partialPointRadius;
}
float previousX = x;
float previousY = y;
x = radius * cosf(currentAngle);
y = radius * sinf(currentAngle);
if (hasRoundness) {
float cp1Theta =
(atan2f(previousY, previousX) - K_PI / 2.0f * angleDir);
float cp1Dx = cosf(cp1Theta);
float cp1Dy = sinf(cp1Theta);
float cp2Theta = (atan2f(y, x) - K_PI / 2.0f * angleDir);
float cp2Dx = cosf(cp2Theta);
float cp2Dy = sinf(cp2Theta);
float cp1Roundness = longSegment ? innerRoundness : outerRoundness;
float cp2Roundness = longSegment ? outerRoundness : innerRoundness;
float cp1Radius = longSegment ? innerRadius : outerRadius;
float cp2Radius = longSegment ? outerRadius : innerRadius;
float cp1x = cp1Radius * cp1Roundness * POLYSTAR_MAGIC_NUMBER *
cp1Dx / points;
float cp1y = cp1Radius * cp1Roundness * POLYSTAR_MAGIC_NUMBER *
cp1Dy / points;
float cp2x = cp2Radius * cp2Roundness * POLYSTAR_MAGIC_NUMBER *
cp2Dx / points;
float cp2y = cp2Radius * cp2Roundness * POLYSTAR_MAGIC_NUMBER *
cp2Dy / points;
if (!vIsZero(partialPointAmount) &&
((i == 0) || (i == numPoints - 1))) {
cp1x *= partialPointAmount;
cp1y *= partialPointAmount;
cp2x *= partialPointAmount;
cp2y *= partialPointAmount;
}
cubicTo(previousX - cp1x + cx, previousY - cp1y + cy, x + cp2x + cx,
y + cp2y + cy, x + cx, y + cy);
} else {
lineTo(x + cx, y + cy);
}
currentAngle += dTheta * angleDir;
longSegment = !longSegment;
}
close();
}
void VPath::VPathData::addPolygon(float points, float radius, float roundness,
float startAngle, float cx, float cy,
VPath::Direction dir)
{
// TODO: Need to support floating point number for number of points
const static float POLYGON_MAGIC_NUMBER = 0.25;
float currentAngle = (startAngle - 90.0f) * K_PI / 180.0f;
float x;
float y;
float anglePerPoint = 2.0f * K_PI / floorf(points);
size_t numPoints = size_t(floorf(points));
float angleDir = ((dir == VPath::Direction::CW) ? 1.0f : -1.0f);
bool hasRoundness = false;
roundness /= 100.0f;
currentAngle = (currentAngle - 90.0f) * K_PI / 180.0f;
x = radius * cosf(currentAngle);
y = radius * sinf(currentAngle);
currentAngle += anglePerPoint * angleDir;
if (vIsZero(roundness)) {
reserve(numPoints + 2, numPoints + 3);
} else {
reserve(numPoints * 3 + 2, numPoints + 3);
hasRoundness = true;
}
moveTo(x + cx, y + cy);
for (size_t i = 0; i < numPoints; i++) {
float previousX = x;
float previousY = y;
x = (radius * cosf(currentAngle));
y = (radius * sinf(currentAngle));
if (hasRoundness) {
float cp1Theta =
(atan2f(previousY, previousX) - K_PI / 2.0f * angleDir);
float cp1Dx = cosf(cp1Theta);
float cp1Dy = sinf(cp1Theta);
float cp2Theta = atan2f(y, x) - K_PI / 2.0f * angleDir;
float cp2Dx = cosf(cp2Theta);
float cp2Dy = sinf(cp2Theta);
float cp1x = radius * roundness * POLYGON_MAGIC_NUMBER * cp1Dx;
float cp1y = radius * roundness * POLYGON_MAGIC_NUMBER * cp1Dy;
float cp2x = radius * roundness * POLYGON_MAGIC_NUMBER * cp2Dx;
float cp2y = radius * roundness * POLYGON_MAGIC_NUMBER * cp2Dy;
cubicTo(previousX - cp1x + cx, previousY - cp1y + cy, x + cp2x + cx,
y + cp2y + cy, x, y);
} else {
lineTo(x + cx, y + cy);
}
currentAngle += anglePerPoint * angleDir;
}
close();
}
void VPath::VPathData::addPath(const VPathData &path, const VMatrix *m)
{
size_t segment = path.segments();
// make sure enough memory available
if (m_points.capacity() < m_points.size() + path.m_points.size())
m_points.reserve(m_points.size() + path.m_points.size());
if (m_elements.capacity() < m_elements.size() + path.m_elements.size())
m_elements.reserve(m_elements.size() + path.m_elements.size());
if (m) {
for (const auto &i : path.m_points) {
m_points.push_back(m->map(i));
}
} else {
std::copy(path.m_points.begin(), path.m_points.end(),
back_inserter(m_points));
}
std::copy(path.m_elements.begin(), path.m_elements.end(),
back_inserter(m_elements));
m_segments += segment;
mLengthDirty = true;
}
V_END_NAMESPACE