Add ImBezierClosestPoint() function which returns a point on bezier curve which is closed to a specified point.

imgui.cpp

@@ -1109,6 +1109,72 @@ void ImGuiIO::ClearInputCharacters()
 // [SECTION] MISC HELPERS/UTILITIES (Geometry, String, Format, Hash, File functions)
 //-----------------------------------------------------------------------------
 
+ImVec2 ImBezierClosestPoint(const ImVec2& p, const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, int num_segments)
+{
+    IM_ASSERT(num_segments > 0);
+    ImVec2 p_last = p1;
+    ImVec2 p_closest;
+    float p_closest_dist2 = FLT_MAX;
+    float t_step = 1.0f / (float)num_segments;
+    for (int i_step = 1; i_step <= num_segments; i_step++)
+    {
+        ImVec2 p_current = ImBezierCalc(p1, p2, p3, p4, t_step * i_step);
+        ImVec2 p_line = ImLineClosestPoint(p_last, p_current, p);
+        float dist2 = ImLengthSqr(p - p_line);
+        if (dist2 < p_closest_dist2)
+        {
+            p_closest = p_line;
+            p_closest_dist2 = dist2;
+        }
+        p_last = p_current;
+    }
+    return p_closest;
+}
+
+// Closely mimics PathBezierToCasteljau() in imgui_draw.cpp
+static void ClosestPointBezierCasteljau(const ImVec2& p, ImVec2& p_closest, ImVec2& p_last, float& p_closest_dist2, float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4, float tess_tol, int level)
+{
+    float dx = x4 - x1;
+    float dy = y4 - y1;
+    float d2 = ((x2 - x4) * dy - (y2 - y4) * dx);
+    float d3 = ((x3 - x4) * dy - (y3 - y4) * dx);
+    d2 = (d2 >= 0) ? d2 : -d2;
+    d3 = (d3 >= 0) ? d3 : -d3;
+    if ((d2+d3) * (d2+d3) < tess_tol * (dx*dx + dy*dy))
+    {
+        ImVec2 p_current(x4, y4);
+        ImVec2 p_line = ImLineClosestPoint(p_last, p_current, p);
+        float dist2 = ImLengthSqr(p - p_line);
+        if (dist2 < p_closest_dist2)
+        {
+            p_closest = p_line;
+            p_closest_dist2 = dist2;
+        }
+        p_last = p_current;
+    }
+    else if (level < 10)
+    {
+        float x12 = (x1+x2)*0.5f,       y12 = (y1+y2)*0.5f;
+        float x23 = (x2+x3)*0.5f,       y23 = (y2+y3)*0.5f;
+        float x34 = (x3+x4)*0.5f,       y34 = (y3+y4)*0.5f;
+        float x123 = (x12+x23)*0.5f,    y123 = (y12+y23)*0.5f;
+        float x234 = (x23+x34)*0.5f,    y234 = (y23+y34)*0.5f;
+        float x1234 = (x123+x234)*0.5f, y1234 = (y123+y234)*0.5f;
+        ClosestPointBezierCasteljau(p, p_closest, p_last, p_closest_dist2, x1, y1, x12, y12, x123, y123, x1234, y1234, tess_tol, level + 1);
+        ClosestPointBezierCasteljau(p, p_closest, p_last, p_closest_dist2, x1234, y1234, x234, y234, x34, y34, x4, y4, tess_tol, level + 1);
+    }
+}
+
+ImVec2 ImBezierClosestPointCasteljau(const ImVec2& p, const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, float tess_tol)
+{
+    IM_ASSERT(tess_tol > 0.0f);
+    ImVec2 p_last = p1;
+    ImVec2 p_closest;
+    float p_closest_dist2 = FLT_MAX;
+    ClosestPointBezierCasteljau(p, p_closest, p_last, p_closest_dist2, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y, p4.x, p4.y, tess_tol, 0);
+    return p_closest;
+}
+
 ImVec2 ImLineClosestPoint(const ImVec2& a, const ImVec2& b, const ImVec2& p)
 {
     ImVec2 ap = p - a;

imgui_draw.cpp

@@ -907,6 +907,17 @@ void ImDrawList::PathArcTo(const ImVec2& center, float radius, float a_min, floa
     }
 }
 
+ImVec2 ImBezierCalc(const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, float t)
+{
+    float u = 1.0f - t;
+    float w1 = u*u*u;
+    float w2 = 3*u*u*t;
+    float w3 = 3*u*t*t;
+    float w4 = t*t*t;
+    return ImVec2(w1*p1.x + w2*p2.x + w3*p3.x + w4*p4.x, w1*p1.y + w2*p2.y + w3*p3.y + w4*p4.y);
+}
+
+// Closely mimicked by ClosestPointBezierCasteljau() in imgui.cpp
 static void PathBezierToCasteljau(ImVector<ImVec2>* path, float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4, float tess_tol, int level)
 {
     float dx = x4 - x1;
@@ -945,15 +956,7 @@ void ImDrawList::PathBezierCurveTo(const ImVec2& p2, const ImVec2& p3, const ImV
     {
         float t_step = 1.0f / (float)num_segments;
         for (int i_step = 1; i_step <= num_segments; i_step++)
-        {
+            _Path.push_back(ImBezierCalc(p1, p2, p3, p4, t_step * i_step));
-            float t = t_step * i_step;
-            float u = 1.0f - t;
-            float w1 = u*u*u;
-            float w2 = 3*u*u*t;
-            float w3 = 3*u*t*t;
-            float w4 = t*t*t;
-            _Path.push_back(ImVec2(w1*p1.x + w2*p2.x + w3*p3.x + w4*p4.x, w1*p1.y + w2*p2.y + w3*p3.y + w4*p4.y));
-        }
     }
 }
 

imgui_internal.h

@@ -340,6 +340,9 @@ static inline float  ImLinearSweep(float current, float target, float speed)
 static inline ImVec2 ImMul(const ImVec2& lhs, const ImVec2& rhs)                { return ImVec2(lhs.x * rhs.x, lhs.y * rhs.y); }
 
 // Helpers: Geometry
+IMGUI_API ImVec2     ImBezierCalc(const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, float t);
+IMGUI_API ImVec2     ImBezierClosestPoint(const ImVec2& p, const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, int num_segments);           // For curves with explicit number of segments
+IMGUI_API ImVec2     ImBezierClosestPointCasteljau(const ImVec2& p, const ImVec2& p1, const ImVec2& p2, const ImVec2& p3, const ImVec2& p4, float tess_tol);    // For auto-tesselated curves, tess_tol = style.CurveTessellationTol
 IMGUI_API ImVec2     ImLineClosestPoint(const ImVec2& a, const ImVec2& b, const ImVec2& p);
 IMGUI_API bool       ImTriangleContainsPoint(const ImVec2& a, const ImVec2& b, const ImVec2& c, const ImVec2& p);
 IMGUI_API ImVec2     ImTriangleClosestPoint(const ImVec2& a, const ImVec2& b, const ImVec2& c, const ImVec2& p);