1 files changed, 245 insertions, 0 deletions
diff --git a/thirdparty/thorvg/src/common/tvgLines.cpp b/thirdparty/thorvg/src/common/tvgLines.cpp
new file mode 100644
index 0000000000..da48f9eae2
--- /dev/null
+++ b/thirdparty/thorvg/src/common/tvgLines.cpp
@@ -0,0 +1,245 @@
+/*
+ * Copyright (c) 2020 - 2024 the ThorVG project. 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 "tvgMath.h"
+#include "tvgLines.h"
+
+#define BEZIER_EPSILON 1e-2f
+
+/************************************************************************/
+/* Internal Class Implementation                                        */
+/************************************************************************/
+
+static float _lineLengthApprox(const Point& pt1, const Point& pt2)
+{
+    /* approximate sqrt(x*x + y*y) using alpha max plus beta min algorithm.
+       With alpha = 1, beta = 3/8, giving results with the largest error less
+       than 7% compared to the exact value. */
+    Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
+    if (diff.x < 0) diff.x = -diff.x;
+    if (diff.y < 0) diff.y = -diff.y;
+    return (diff.x > diff.y) ? (diff.x + diff.y * 0.375f) : (diff.y + diff.x * 0.375f);
+}
+
+
+static float _lineLength(const Point& pt1, const Point& pt2)
+{
+    Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
+    return sqrtf(diff.x * diff.x + diff.y * diff.y);
+}
+
+
+template<typename LengthFunc>
+float _bezLength(const Bezier& cur, LengthFunc lineLengthFunc)
+{
+    Bezier left, right;
+    auto len = lineLengthFunc(cur.start, cur.ctrl1) + lineLengthFunc(cur.ctrl1, cur.ctrl2) + lineLengthFunc(cur.ctrl2, cur.end);
+    auto chord = lineLengthFunc(cur.start, cur.end);
+
+    if (fabsf(len - chord) > BEZIER_EPSILON) {
+        tvg::bezSplit(cur, left, right);
+        return _bezLength(left, lineLengthFunc) + _bezLength(right, lineLengthFunc);
+    }
+    return len;
+}
+
+
+template<typename LengthFunc>
+float _bezAt(const Bezier& bz, float at, float length, LengthFunc lineLengthFunc)
+{
+    auto biggest = 1.0f;
+    auto smallest = 0.0f;
+    auto t = 0.5f;
+
+    //just in case to prevent an infinite loop
+    if (at <= 0) return 0.0f;
+    if (at >= length) return 1.0f;
+
+    while (true) {
+        auto right = bz;
+        Bezier left;
+        bezSplitLeft(right, t, left);
+        length = _bezLength(left, lineLengthFunc);
+        if (fabsf(length - at) < BEZIER_EPSILON || fabsf(smallest - biggest) < BEZIER_EPSILON) {
+            break;
+        }
+        if (length < at) {
+            smallest = t;
+            t = (t + biggest) * 0.5f;
+        } else {
+            biggest = t;
+            t = (smallest + t) * 0.5f;
+        }
+    }
+    return t;
+}
+
+
+/************************************************************************/
+/* External Class Implementation                                        */
+/************************************************************************/
+
+namespace tvg
+{
+
+float lineLength(const Point& pt1, const Point& pt2)
+{
+    return _lineLength(pt1, pt2);
+}
+
+
+void lineSplitAt(const Line& cur, float at, Line& left, Line& right)
+{
+    auto len = lineLength(cur.pt1, cur.pt2);
+    auto dx = ((cur.pt2.x - cur.pt1.x) / len) * at;
+    auto dy = ((cur.pt2.y - cur.pt1.y) / len) * at;
+    left.pt1 = cur.pt1;
+    left.pt2.x = left.pt1.x + dx;
+    left.pt2.y = left.pt1.y + dy;
+    right.pt1 = left.pt2;
+    right.pt2 = cur.pt2;
+}
+
+
+void bezSplit(const Bezier& cur, Bezier& left, Bezier& right)
+{
+    auto c = (cur.ctrl1.x + cur.ctrl2.x) * 0.5f;
+    left.ctrl1.x = (cur.start.x + cur.ctrl1.x) * 0.5f;
+    right.ctrl2.x = (cur.ctrl2.x + cur.end.x) * 0.5f;
+    left.start.x = cur.start.x;
+    right.end.x = cur.end.x;
+    left.ctrl2.x = (left.ctrl1.x + c) * 0.5f;
+    right.ctrl1.x = (right.ctrl2.x + c) * 0.5f;
+    left.end.x = right.start.x = (left.ctrl2.x + right.ctrl1.x) * 0.5f;
+
+    c = (cur.ctrl1.y + cur.ctrl2.y) * 0.5f;
+    left.ctrl1.y = (cur.start.y + cur.ctrl1.y) * 0.5f;
+    right.ctrl2.y = (cur.ctrl2.y + cur.end.y) * 0.5f;
+    left.start.y = cur.start.y;
+    right.end.y = cur.end.y;
+    left.ctrl2.y = (left.ctrl1.y + c) * 0.5f;
+    right.ctrl1.y = (right.ctrl2.y + c) * 0.5f;
+    left.end.y = right.start.y = (left.ctrl2.y + right.ctrl1.y) * 0.5f;
+}
+
+
+float bezLength(const Bezier& cur)
+{
+    return _bezLength(cur, _lineLength);
+}
+
+
+float bezLengthApprox(const Bezier& cur)
+{
+    return _bezLength(cur, _lineLengthApprox);
+}
+
+
+void bezSplitLeft(Bezier& cur, float at, Bezier& left)
+{
+    left.start = cur.start;
+
+    left.ctrl1.x = cur.start.x + at * (cur.ctrl1.x - cur.start.x);
+    left.ctrl1.y = cur.start.y + at * (cur.ctrl1.y - cur.start.y);
+
+    left.ctrl2.x = cur.ctrl1.x + at * (cur.ctrl2.x - cur.ctrl1.x); //temporary holding spot
+    left.ctrl2.y = cur.ctrl1.y + at * (cur.ctrl2.y - cur.ctrl1.y); //temporary holding spot
+
+    cur.ctrl2.x = cur.ctrl2.x + at * (cur.end.x - cur.ctrl2.x);
+    cur.ctrl2.y = cur.ctrl2.y + at * (cur.end.y - cur.ctrl2.y);
+
+    cur.ctrl1.x = left.ctrl2.x + at * (cur.ctrl2.x - left.ctrl2.x);
+    cur.ctrl1.y = left.ctrl2.y + at * (cur.ctrl2.y - left.ctrl2.y);
+
+    left.ctrl2.x = left.ctrl1.x + at * (left.ctrl2.x - left.ctrl1.x);
+    left.ctrl2.y = left.ctrl1.y + at * (left.ctrl2.y - left.ctrl1.y);
+
+    left.end.x = cur.start.x = left.ctrl2.x + at * (cur.ctrl1.x - left.ctrl2.x);
+    left.end.y = cur.start.y = left.ctrl2.y + at * (cur.ctrl1.y - left.ctrl2.y);
+}
+
+
+float bezAt(const Bezier& bz, float at, float length)
+{
+    return _bezAt(bz, at, length, _lineLength);
+}
+
+
+float bezAtApprox(const Bezier& bz, float at, float length)
+{
+    return _bezAt(bz, at, length, _lineLengthApprox);
+}
+
+
+void bezSplitAt(const Bezier& cur, float at, Bezier& left, Bezier& right)
+{
+    right = cur;
+    auto t = bezAt(right, at, bezLength(right));
+    bezSplitLeft(right, t, left);
+}
+
+
+Point bezPointAt(const Bezier& bz, float t)
+{
+    Point cur;
+    auto it = 1.0f - t;
+
+    auto ax = bz.start.x * it + bz.ctrl1.x * t;
+    auto bx = bz.ctrl1.x * it + bz.ctrl2.x * t;
+    auto cx = bz.ctrl2.x * it + bz.end.x * t;
+    ax = ax * it + bx * t;
+    bx = bx * it + cx * t;
+    cur.x = ax * it + bx * t;
+
+    float ay = bz.start.y * it + bz.ctrl1.y * t;
+    float by = bz.ctrl1.y * it + bz.ctrl2.y * t;
+    float cy = bz.ctrl2.y * it + bz.end.y * t;
+    ay = ay * it + by * t;
+    by = by * it + cy * t;
+    cur.y = ay * it + by * t;
+
+    return cur;
+}
+
+
+float bezAngleAt(const Bezier& bz, float t)
+{
+    if (t < 0 || t > 1) return 0;
+
+    //derivate
+    // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 *
+    // t^2) * p2 + t^2 * p3)
+    float mt = 1.0f - t;
+    float d = t * t;
+    float a = -mt * mt;
+    float b = 1 - 4 * t + 3 * d;
+    float c = 2 * t - 3 * d;
+
+    Point pt ={a * bz.start.x + b * bz.ctrl1.x + c * bz.ctrl2.x + d * bz.end.x, a * bz.start.y + b * bz.ctrl1.y + c * bz.ctrl2.y + d * bz.end.y};
+    pt.x *= 3;
+    pt.y *= 3;
+
+    return mathRad2Deg(atan2(pt.x, pt.y));
+}
+
+
+}