LibWeb: Add CanvasPath arcTo support

Adds initial CanvasPath arcTo support for 2D rendering contexts
https://html.spec.whatwg.org/multipage/canvas.html#dom-context-2d-arcto

Userland/Libraries/LibWeb/HTML/Canvas/CanvasPath.cpp

@@ -120,6 +120,78 @@ WebIDL::ExceptionOr<void> CanvasPath::ellipse(float x, float y, float radius_x,
     return {};
 }
 
+// https://html.spec.whatwg.org/multipage/canvas.html#dom-context-2d-arcto
+WebIDL::ExceptionOr<void> CanvasPath::arc_to(double x1, double y1, double x2, double y2, double radius)
+{
+    // 1. If any of the arguments are infinite or NaN, then return.
+    if (!isfinite(x1) || !isfinite(y1) || !isfinite(x2) || !isfinite(y2) || !isfinite(radius))
+        return {};
+
+    // 2. Ensure there is a subpath for (x1, y1).
+    auto transform = active_transform();
+    m_path.ensure_subpath(transform.map(Gfx::FloatPoint { x1, y1 }));
+
+    // 3. If radius is negative, then throw an "IndexSizeError" DOMException.
+    if (radius < 0)
+        return WebIDL::IndexSizeError::create(m_self->realm(), MUST(String::formatted("The radius provided ({}) is negative.", radius)));
+
+    // 4. Let the point (x0, y0) be the last point in the subpath,
+    //    transformed by the inverse of the current transformation matrix
+    //    (so that it is in the same coordinate system as the points passed to the method).
+    // Point (x0, y0)
+    auto p0 = m_path.last_point();
+    // Point (x1, y1)
+    auto p1 = transform.map(Gfx::FloatPoint { x1, y1 });
+    // Point (x2, y2)
+    auto p2 = transform.map(Gfx::FloatPoint { x2, y2 });
+
+    // 5. If the point (x0, y0) is equal to the point (x1, y1),
+    //    or if the point (x1, y1) is equal to the point (x2, y2),
+    //    or if radius is zero, then add the point (x1, y1) to the subpath,
+    //    and connect that point to the previous point (x0, y0) by a straight line.
+    if (p0 == p1 || p1 == p2 || radius == 0) {
+        m_path.line_to(p1);
+        return {};
+    }
+
+    auto v1 = Gfx::FloatVector2 { p0.x() - p1.x(), p0.y() - p1.y() };
+    auto v2 = Gfx::FloatVector2 { p2.x() - p1.x(), p2.y() - p1.y() };
+    auto cos_theta = v1.dot(v2) / (v1.length() * v2.length());
+    // 6. Otherwise, if the points (x0, y0), (x1, y1), and (x2, y2) all lie on a single straight line,
+    //    then add the point (x1, y1) to the subpath,
+    //    and connect that point to the previous point (x0, y0) by a straight line.
+    if (-1 == cos_theta || 1 == cos_theta) {
+        m_path.line_to(p1);
+        return {};
+    }
+
+    // 7. Otherwise, let The Arc be the shortest arc given by circumference of the circle that has radius radius,
+    // and that has one point tangent to the half-infinite line that crosses the point (x0, y0) and ends at the point (x1, y1),
+    // and that has a different point tangent to the half-infinite line that ends at the point (x1, y1) and crosses the point (x2, y2).
+    // The points at which this circle touches these two lines are called the start and end tangent points respectively.
+    auto adjacent = radius / static_cast<double>(tan(acos(cos_theta) / 2));
+    auto factor1 = adjacent / static_cast<double>(v1.length());
+    auto x3 = static_cast<double>(p1.x()) + factor1 * static_cast<double>(p0.x() - p1.x());
+    auto y3 = static_cast<double>(p1.y()) + factor1 * static_cast<double>(p0.y() - p1.y());
+    auto start_tangent = Gfx::FloatPoint { x3, y3 };
+
+    auto factor2 = adjacent / static_cast<double>(v2.length());
+    auto x4 = static_cast<double>(p1.x()) + factor2 * static_cast<double>(p2.x() - p1.x());
+    auto y4 = static_cast<double>(p1.y()) + factor2 * static_cast<double>(p2.y() - p1.y());
+    auto end_tangent = Gfx::FloatPoint { x4, y4 };
+
+    // Connect the point (x0, y0) to the start tangent point by a straight line, adding the start tangent point to the subpath.
+    m_path.line_to(start_tangent);
+
+    bool const large_arc = false; // always small since tangent points define arc endpoints and lines meet at (x1, y1)
+    auto cross_product = v1.x() * v2.y() - v1.y() * v2.x();
+    bool const sweep = cross_product < 0; // right-hand rule, true means clockwise
+
+    // and then connect the start tangent point to the end tangent point by The Arc, adding the end tangent point to the subpath.
+    m_path.arc_to(end_tangent, radius, large_arc, sweep);
+    return {};
+}
+
 void CanvasPath::rect(float x, float y, float width, float height)
 {
     auto transform = active_transform();