Improve on automatic circle segment count calculation. (#3808)

imgui.cpp

@@ -986,7 +986,7 @@ ImGuiStyle::ImGuiStyle()
     AntiAliasedLinesUseTex  = true;             // Enable anti-aliased lines/borders using textures where possible. Require backend to render with bilinear filtering.
     AntiAliasedFill         = true;             // Enable anti-aliased filled shapes (rounded rectangles, circles, etc.).
     CurveTessellationTol    = 1.25f;            // Tessellation tolerance when using PathBezierCurveTo() without a specific number of segments. Decrease for highly tessellated curves (higher quality, more polygons), increase to reduce quality.
-    CircleSegmentMaxError   = 1.60f;            // Maximum error (in pixels) allowed when using AddCircle()/AddCircleFilled() or drawing rounded corner rectangles with no explicit segment count specified. Decrease for higher quality but more geometry.
+    CircleTessellationMaxError = 0.25f;         // Maximum error (in pixels) allowed when using AddCircle()/AddCircleFilled() or drawing rounded corner rectangles with no explicit segment count specified. Decrease for higher quality but more geometry.
 
     // Default theme
     ImGui::StyleColorsDark(this);
@@ -3878,7 +3878,7 @@ void ImGui::NewFrame()
         virtual_space.Add(g.Viewports[n]->GetMainRect());
     g.DrawListSharedData.ClipRectFullscreen = virtual_space.ToVec4();
     g.DrawListSharedData.CurveTessellationTol = g.Style.CurveTessellationTol;
-    g.DrawListSharedData.SetCircleSegmentMaxError(g.Style.CircleSegmentMaxError);
+    g.DrawListSharedData.SetCircleTessellationMaxError(g.Style.CircleTessellationMaxError);
     g.DrawListSharedData.InitialFlags = ImDrawListFlags_None;
     if (g.Style.AntiAliasedLines)
         g.DrawListSharedData.InitialFlags |= ImDrawListFlags_AntiAliasedLines;
@@ -7056,7 +7056,7 @@ static void ImGui::ErrorCheckNewFrameSanityChecks()
     IM_ASSERT(g.IO.Fonts->Fonts.Size > 0                                && "Font Atlas not built. Did you call io.Fonts->GetTexDataAsRGBA32() / GetTexDataAsAlpha8()?");
     IM_ASSERT(g.IO.Fonts->Fonts[0]->IsLoaded()                          && "Font Atlas not built. Did you call io.Fonts->GetTexDataAsRGBA32() / GetTexDataAsAlpha8()?");
     IM_ASSERT(g.Style.CurveTessellationTol > 0.0f                       && "Invalid style setting!");
-    IM_ASSERT(g.Style.CircleSegmentMaxError > 0.0f                      && "Invalid style setting!");
+    IM_ASSERT(g.Style.CircleTessellationMaxError  > 0.0f                && "Invalid style setting!");
     IM_ASSERT(g.Style.Alpha >= 0.0f && g.Style.Alpha <= 1.0f            && "Invalid style setting!"); // Allows us to avoid a few clamps in color computations
     IM_ASSERT(g.Style.WindowMinSize.x >= 1.0f && g.Style.WindowMinSize.y >= 1.0f && "Invalid style setting.");
     IM_ASSERT(g.Style.WindowMenuButtonPosition == ImGuiDir_None || g.Style.WindowMenuButtonPosition == ImGuiDir_Left || g.Style.WindowMenuButtonPosition == ImGuiDir_Right);

imgui.h

@@ -1723,7 +1723,7 @@ struct ImGuiStyle
     bool        AntiAliasedLinesUseTex;     // Enable anti-aliased lines/borders using textures where possible. Require backend to render with bilinear filtering. Latched at the beginning of the frame (copied to ImDrawList).
     bool        AntiAliasedFill;            // Enable anti-aliased edges around filled shapes (rounded rectangles, circles, etc.). Disable if you are really tight on CPU/GPU. Latched at the beginning of the frame (copied to ImDrawList).
     float       CurveTessellationTol;       // Tessellation tolerance when using PathBezierCurveTo() without a specific number of segments. Decrease for highly tessellated curves (higher quality, more polygons), increase to reduce quality.
-    float       CircleSegmentMaxError;      // Maximum error (in pixels) allowed when using AddCircle()/AddCircleFilled() or drawing rounded corner rectangles with no explicit segment count specified. Decrease for higher quality but more geometry.
+    float       CircleTessellationMaxError; // Maximum error (in pixels) allowed when using AddCircle()/AddCircleFilled() or drawing rounded corner rectangles with no explicit segment count specified. Decrease for higher quality but more geometry.
     ImVec4      Colors[ImGuiCol_COUNT];
 
     IMGUI_API ImGuiStyle();
@@ -2463,6 +2463,7 @@ struct ImDrawList
     IMGUI_API void  _OnChangedClipRect();
     IMGUI_API void  _OnChangedTextureID();
     IMGUI_API void  _OnChangedVtxOffset();
+    IMGUI_API int   _CalcCircleAutoSegmentCount(float radius) const;
 };
 
 // All draw data to render a Dear ImGui frame

imgui_demo.cpp

@@ -6034,22 +6034,44 @@ void ImGui::ShowStyleEditor(ImGuiStyle* ref)
             if (style.CurveTessellationTol < 0.10f) style.CurveTessellationTol = 0.10f;
 
             // When editing the "Circle Segment Max Error" value, draw a preview of its effect on auto-tessellated circles.
-            ImGui::DragFloat("Circle Segment Max Error", &style.CircleSegmentMaxError, 0.01f, 0.10f, 10.0f, "%.2f");
+            ImGui::DragFloat("Circle Tessellation Max Error", &style.CircleTessellationMaxError , 0.005f, 0.10f, 10.0f, "%.2f", ImGuiSliderFlags_AlwaysClamp);
             if (ImGui::IsItemActive())
             {
                 ImGui::SetNextWindowPos(ImGui::GetCursorScreenPos());
                 ImGui::BeginTooltip();
-                ImVec2 p = ImGui::GetCursorScreenPos();
+                ImGui::TextUnformatted("N - number of segments");
+                ImGui::TextUnformatted("R - radius");
+                ImGui::Spacing();
                 ImDrawList* draw_list = ImGui::GetWindowDrawList();
-                float RAD_MIN = 10.0f, RAD_MAX = 80.0f;
-                float off_x = 10.0f;
-                for (int n = 0; n < 7; n++)
+                const float min_widget_width = ImGui::CalcTextSize("N: MM\nR: MM.MM").x;
+                float RAD_MIN = 5.0f, RAD_MAX = 80.0f;
+                for (int n = 0; n < 9; n++)
                 {
-                    const float rad = RAD_MIN + (RAD_MAX - RAD_MIN) * (float)n / (7.0f - 1.0f);
-                    draw_list->AddCircle(ImVec2(p.x + off_x + rad, p.y + RAD_MAX), rad, ImGui::GetColorU32(ImGuiCol_Text), 0);
-                    off_x += 10.0f + rad * 2.0f;
+                    const float rad = RAD_MIN + (RAD_MAX - RAD_MIN) * (float)n / (9.0f - 1.0f);
+
+                    const int segment_count = draw_list->_CalcCircleAutoSegmentCount(rad);
+
+                    ImGui::BeginGroup();
+                    ImGui::Text("R: %.f", rad);
+                    ImGui::Text("N: %d", segment_count);
+
+                    const float circle_diameter = rad * 2.0f;
+                    const float canvas_width    = IM_MAX(min_widget_width, circle_diameter);
+                    const float offset_x        = floorf(canvas_width * 0.5f);
+                    const float offset_y        = floorf(RAD_MAX);
+                    const ImVec2 p              = ImGui::GetCursorScreenPos();
+                    draw_list->AddCircle(ImVec2(p.x + offset_x, p.y + offset_y), rad, ImGui::GetColorU32(ImGuiCol_Text));
+
+                    ImGui::Dummy(ImVec2(canvas_width, RAD_MAX * 2));
+                    ImGui::Text("N: %d", segment_count);
+
+                    const ImVec2 p2             = ImGui::GetCursorScreenPos();
+                    draw_list->AddCircleFilled(ImVec2(p2.x + offset_x, p2.y + offset_y), rad, ImGui::GetColorU32(ImGuiCol_Text));
+
+                    ImGui::Dummy(ImVec2(canvas_width, RAD_MAX * 2));
+                    ImGui::EndGroup();
+                    ImGui::SameLine();
                 }
-                ImGui::Dummy(ImVec2(off_x, RAD_MAX * 2.0f));
                 ImGui::EndTooltip();
             }
             ImGui::SameLine();

imgui_draw.cpp

@@ -376,7 +376,7 @@ ImDrawListSharedData::ImDrawListSharedData()
     }
 }
 
-void ImDrawListSharedData::SetCircleSegmentMaxError(float max_error)
+void ImDrawListSharedData::SetCircleTessellationMaxError(float max_error)
 {
     if (CircleSegmentMaxError == max_error)
         return;
@@ -384,8 +384,7 @@ void ImDrawListSharedData::SetCircleSegmentMaxError(float max_error)
     for (int i = 0; i < IM_ARRAYSIZE(CircleSegmentCounts); i++)
     {
         const float radius = (float)i;
-        const int segment_count = (i > 0) ? IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(radius, CircleSegmentMaxError) : 0;
-        CircleSegmentCounts[i] = (ImU8)ImMin(segment_count, 255);
+        CircleSegmentCounts[i] = (ImU8)((i > 0) ? IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(radius, CircleSegmentMaxError) : 0);
     }
 }
 
@@ -543,6 +542,21 @@ void ImDrawList::_OnChangedVtxOffset()
     curr_cmd->VtxOffset = _CmdHeader.VtxOffset;
 }
 
+int ImDrawList::_CalcCircleAutoSegmentCount(float radius) const
+{
+    int num_segments = 0;
+
+    const int  radius_idx = (int)ImCeil(radius); // Use ceil to never reduce accuracy
+
+    // Automatic segment count
+    if (radius_idx < IM_ARRAYSIZE(_Data->CircleSegmentCounts))
+        num_segments = _Data->CircleSegmentCounts[radius_idx]; // Use cached value
+    else
+        num_segments = IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(radius, _Data->CircleSegmentMaxError);
+
+    return num_segments;
+}
+
 // Render-level scissoring. This is passed down to your render function but not used for CPU-side coarse clipping. Prefer using higher-level ImGui::PushClipRect() to affect logic (hit-testing and widget culling)
 void ImDrawList::PushClipRect(ImVec2 cr_min, ImVec2 cr_max, bool intersect_with_current_clip_rect)
 {
@@ -1286,11 +1300,7 @@ void ImDrawList::AddCircle(const ImVec2& center, float radius, ImU32 col, int nu
     if (num_segments <= 0)
     {
         // Automatic segment count
-        const int radius_idx = (int)radius;
-        if (radius_idx < IM_ARRAYSIZE(_Data->CircleSegmentCounts))
-            num_segments = _Data->CircleSegmentCounts[radius_idx]; // Use cached value
-        else
-            num_segments = IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(radius, _Data->CircleSegmentMaxError);
+        num_segments = _CalcCircleAutoSegmentCount(radius);
     }
     else
     {
@@ -1316,11 +1326,7 @@ void ImDrawList::AddCircleFilled(const ImVec2& center, float radius, ImU32 col,
     if (num_segments <= 0)
     {
         // Automatic segment count
-        const int radius_idx = (int)radius;
-        if (radius_idx < IM_ARRAYSIZE(_Data->CircleSegmentCounts))
-            num_segments = _Data->CircleSegmentCounts[radius_idx]; // Use cached value
-        else
-            num_segments = IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(radius, _Data->CircleSegmentMaxError);
+        num_segments = _CalcCircleAutoSegmentCount(radius);
     }
     else
     {

imgui_internal.h

@@ -617,10 +617,29 @@ struct IMGUI_API ImChunkStream
 //-----------------------------------------------------------------------------
 
 // ImDrawList: Helper function to calculate a circle's segment count given its radius and a "maximum error" value.
-// FIXME: the minimum number of auto-segment may be undesirably high for very small radiuses (e.g. 1.0f)
-#define IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MIN                     12
+//
+// Estimation of number of circle segment based on error is derived using method described in
+// this post (https://stackoverflow.com/a/2244088/15194693).
+// Number of segments (N) is calculated using equation:
+//
+//            +-                     -+
+//            |           pi          |
+//   N = ceil | --------------------- |     where r > 0, error <= r
+//            |  acos(1 - error / r)  |
+//            +-                     -+
+//
+// Note:
+//     Equation is significantly simpler that one in the post thanks for choosing segment
+//     that is perpendicular to X axis. Follow steps in the article from this starting condition
+//     and you will get this result.
+//
+// Rendering circles with an odd number of segments, while mathematically correct will produce
+// asymmetrical results on the raster grid. Therefore we're rounding N to next even number.
+// (7 became 8, 11 became 12, but 8 will still be 8).
+//
+#define IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MIN                     4
 #define IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MAX                     512
-#define IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(_RAD,_MAXERROR)    ImClamp((int)((IM_PI * 2.0f) / ImAcos(((_RAD) - (_MAXERROR)) / (_RAD))), IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MIN, IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MAX)
+#define IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_CALC(_RAD,_MAXERROR)    ImClamp((((int)ImCeil(IM_PI / ImAcos(1 - ImMin((_MAXERROR), (_RAD)) / (_RAD))) + 1) / 2) * 2, IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MIN, IM_DRAWLIST_CIRCLE_AUTO_SEGMENT_MAX)
 
 // ImDrawList: You may set this to higher values (e.g. 2 or 3) to increase tessellation of fast rounded corners path.
 #ifndef IM_DRAWLIST_ARCFAST_TESSELLATION_MULTIPLIER
@@ -641,11 +660,11 @@ struct IMGUI_API ImDrawListSharedData
 
     // [Internal] Lookup tables
     ImVec2          ArcFastVtx[12 * IM_DRAWLIST_ARCFAST_TESSELLATION_MULTIPLIER];  // FIXME: Bake rounded corners fill/borders in atlas
-    ImU8            CircleSegmentCounts[64];    // Precomputed segment count for given radius before we calculate it dynamically (to avoid calculation overhead)
-    const ImVec4*   TexUvLines;                 // UV of anti-aliased lines in the atlas
+    ImU8            CircleSegmentCounts[64];                // Precomputed segment count for given radius before we calculate it dynamically (to avoid calculation overhead)
+    const ImVec4*   TexUvLines;                             // UV of anti-aliased lines in the atlas
 
     ImDrawListSharedData();
-    void SetCircleSegmentMaxError(float max_error);
+    void SetCircleTessellationMaxError(float max_error);
 };
 
 struct ImDrawDataBuilder