Path.cpp

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/*
   Copyright 2022 Rishi Challa
 
   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.
*/
 
#include "Path.hpp"
 
#include <Kale/Core/Logger/Logger.hpp>
 
#include <limits>
 
using namespace Kale;
 
Path::Path() {
    // Empty Body
}
 
Path::Path(size_t n) : beziers(n) {
    // Empty Body
}
 
Path::Path(const std::vector<CubicBezier>& beziers) : beziers(beziers) {
    // Empty Body
}
 
Path::Path(const std::vector<Vector2f>& lines, float cornerRadius) {
    std::vector<std::pair<Vector2f, float>> l(lines.size());
    std::transform(lines.begin(), lines.end(), l.begin(), [&](const Vector2f& pos) -> std::pair<Vector2f, float> {
        return std::make_pair(pos, cornerRadius);
    });
    roundCorners(l);
}
 
Path::Path(const std::vector<std::pair<Vector2f, float>>& lines) {
    roundCorners(lines);
}
 
void Path::roundCorners(const std::vector<std::pair<Vector2f, float>>& lines) {
 
    // Loop through all of the corners and attempt to round them
    moveTo(lines[0].first);
 
    for (size_t i = 0; i < lines.size(); i++) {
 
        // Get the radius for this corner
        float radius = lines[i].second;
 
        // Get the corner, next, and previous points
        Vector2f corner = lines[i].first;
        Vector2f prev = i != 0 ? lines[i-1].first : lines.back().first;
        Vector2f next = i+1 < lines.size() ? lines[i+1].first : lines.front().first;
 
        // Calculate the cross product to see if our angle is acute or obtuse
        float cp = (prev - corner).cross(next - corner);
        if (isFloating0(cp) || radius <= 0.0f) {
            lineTo(corner);
            continue;
        }
 
        Vector2f prevOffset, nextOffset;
        bool clockwise;
 
        // Acute angle
        if (cp < 0) {
            clockwise = false;
            prevOffset = (prev - corner).rotateClockwise().normalized() * radius;
            nextOffset = (next - corner).rotateCounterClockwise().normalized() * radius;
        }
        // Obtuse angle
        else {
            clockwise = true;
            prevOffset = (prev - corner).rotateCounterClockwise().normalized() * radius;
            nextOffset = (next - corner).rotateClockwise().normalized() * radius;
        }
 
        // Create 2 parallel lines next to the previous - corner & next - corner lines
        Vector2f prevLp0 = prev + prevOffset;
        Vector2f prevLp1 = corner + prevOffset;
        Vector2f nextLp0 = next + nextOffset;
        Vector2f nextLp1 = corner + nextOffset;
 
        Vector2f prevDist = prevLp1 - prevLp0;
        Vector2f nextDist = nextLp1 - nextLp0;
 
        // Calculate the times of their intersection
        float prevT = (nextLp0 - prevLp0).cross(nextDist / prevDist.cross(nextDist));
        float nextT = (nextLp0 - prevLp0).cross(prevDist / prevDist.cross(nextDist));
 
        Vector2f center = prevLp0 + prevDist * prevT;
        Vector2f truePrev = prev + prevDist * prevT;
        Vector2f trueNext = next + nextDist * nextT;
 
        lineTo(truePrev);
        arcTo(trueNext, center, clockwise);
    }
 
    closePath();
}
 
Rect Path::getBoundingBox() const {
    Vector2f topLeft = Vector2f::max();
    Vector2f bottomRight = Vector2f::min();
    
    for (const CubicBezier& bezier : beziers) {
        for (const Vector2f& point : {bezier.start, bezier.controlPoint1, bezier.controlPoint2, bezier.end}) {
            if (point.x < topLeft.x) topLeft.x = point.x;
            if (point.y < topLeft.y) topLeft.y = point.y;
            if (point.x > bottomRight.x) bottomRight.x = point.x;
            if (point.y > bottomRight.y) bottomRight.y = point.y;
        }
    }
 
    return {topLeft, bottomRight};
}
 
void Path::operator+=(const Path& other) {
    klAssert(other.beziers.size() == beziers.size());
    for (size_t i = 0; i < beziers.size(); i++) {
        beziers[i].start += other.beziers[i].start;
        beziers[i].controlPoint1 += other.beziers[i].controlPoint1;
        beziers[i].controlPoint2 += other.beziers[i].controlPoint2;
        beziers[i].end += other.beziers[i].end;
    }
}
 
Path Path::operator*(float value) const {
    Path path(*this);
    for (CubicBezier& bezier : path.beziers) {
        bezier.start *= value;
        bezier.controlPoint1 *= value;
        bezier.controlPoint2 *= value;
        bezier.end *= value;
    }
    return path;
}
 
void Path::moveTo(Vector2f pos) {
    beziers.clear();
    beziers.push_back(CubicBezier{pos, Vector2f::zero(), Vector2f::zero(), Vector2f::zero()});
}
 
void Path::lineTo(Vector2f pos) {
    beziers.back().controlPoint1 = beziers.back().start;
    beziers.back().controlPoint2 = pos;
    beziers.back().end = pos;
    beziers.push_back(CubicBezier{pos, Vector2f::zero(), Vector2f::zero(), Vector2f::zero()});
}
 
void Path::bezierTo(Vector2f controlPoint1, Vector2f controlPoint2, Vector2f end) {
    beziers.back().controlPoint1 = controlPoint1;
    beziers.back().controlPoint2 = controlPoint2;
    beziers.back().end = end;
    beziers.push_back(CubicBezier{end, Vector2f::zero(), Vector2f::zero(), Vector2f::zero()});
}
 
void Path::arcTo(Vector2f end, Vector2f center, bool clockwise) {
    // Calculate the number of segments we need to approximate the curve (1 - 0:90, 2 - 90:180, 3 - 180:270, 4 - 270:360)
    float radius = (end - center).magnitude();
    float angle = (beziers.back().start - center).signedAngle(end - center);
    int numsegments;
    if (angle > 0) numsegments = static_cast<int>(ceil(angle / (0.5f * PI)));
    else numsegments = static_cast<int>(ceil((angle + 2.0f * PI) / (0.5f * PI)));
 
    if (clockwise) numsegments = std::max(4 - numsegments, 1);
 
    // Prep for loop
    float a = angle * (1.0f / static_cast<float>(numsegments));
    if (clockwise) a += 2.0f * PI;
 
    // This is a constant needed to approximate a circle with beziers - 
    // https://stackoverflow.com/questions/1734745/how-to-create-circle-with-bézier-curves
    float bezierArcApprox = (4.0f / 3.0f) * tan(PI / (2.0f * (static_cast<float>(numsegments) * 2.0f * PI / angle)));
 
    // Loop through the segments
    for (size_t i = 0; i < static_cast<size_t>(numsegments); i++) {
 
        // Rotate the end of the last segment about the center
        CubicBezier& last = beziers.back();
        float c = cos(a);
        float s = sin(a);
        Vector2f n = Vector2f(
            (c * (last.start.x - center.x)) - (s * (last.start.y - center.y)),
            (s * (last.start.x - center.x)) + (c * (last.start.y - center.y))
        ) + center;
 
        // Create the bezier approximation
        last.controlPoint1 = last.start + (center - last.start).rotateClockwise().normalized() * bezierArcApprox * radius;
        last.controlPoint2 = n + (center - n).rotateCounterClockwise().normalized() * bezierArcApprox * radius;
        last.end = n;
        beziers.push_back(CubicBezier{n, Vector2f::zero(), Vector2f::zero(), Vector2f::zero()});
    }
}
 
void Path::closePath() {
    if (beziers.front().controlPoint1 == beziers.front().start) beziers.front().controlPoint1 = beziers.back().start;
    beziers.front().start = beziers.back().start;
    beziers.pop_back();
}
 
std::ostream& Kale::operator<<(std::ostream& os, const CubicBezier& bezier) {
    os << "CubicBezier(" << bezier.start << ", " << bezier.controlPoint1 << ", " << bezier.controlPoint2 << ", " << bezier.end << ")";
    return os;
}
 
std::ostream& Kale::operator<<(std::ostream& os, const Path& path) {
    os << "Path(\n";
    for (const CubicBezier& bezier : path.beziers) os << bezier << "\n";
    os << ")";
    return os;
}