[PATCH 2/2] d2d1: Implement ellipse geometry simplification.

[Nikolay Sivov]

From: Nikolay Sivov

Signed-off-by: Nikolay Sivov 
---
 dlls/d2d1/geometry.c | 75 ++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 73 insertions(+), 2 deletions(-)

diff --git a/dlls/d2d1/geometry.c b/dlls/d2d1/geometry.c
index 9867e6171e7..09c6fbcc956 100644
--- a/dlls/d2d1/geometry.c
+++ b/dlls/d2d1/geometry.c
@@ -4089,10 +4089,81 @@ static HRESULT STDMETHODCALLTYPE d2d_ellipse_geometry_Simplify(ID2D1EllipseGeome
         D2D1_GEOMETRY_SIMPLIFICATION_OPTION option, const D2D1_MATRIX_3X2_F *transform, float tolerance,
         ID2D1SimplifiedGeometrySink *sink)
 {
-    FIXME("iface %p, option %#x, transform %p, tolerance %.8e, sink %p stub!\n",
+    struct d2d_geometry *geometry = impl_from_ID2D1EllipseGeometry(iface);
+    const D2D1_ELLIPSE *ellipse = &geometry->u.ellipse.ellipse;
+    struct d2d_figure figure = { 0 };
+    D2D1_BEZIER_SEGMENT segments[4];
+    D2D1_POINT_2F start_point;
+    D2D1_MATRIX_3X2_F m;
+    unsigned int i;
+    float coeff;
+
+    TRACE("iface %p, option %#x, transform %p, tolerance %.8e, sink %p.\n",
             iface, option, transform, tolerance, sink);

-    return E_NOTIMPL;
+    /* Use four Bézier segments to approximate a unit circle.
+       Endpoints tangents are tangential to the circle. Endpoints and the midpoint
+       are lying on the circle. */
+    coeff = 4.0f * (M_SQRT2 - 1.0f) / 3.0f;
+
+    start_point.x = -1.0f;
+    start_point.y = 0.0f;
+
+    segments[0].point1.x =  -1.0f;
+    segments[0].point1.y = -coeff;
+    segments[0].point2.x = -coeff;
+    segments[0].point2.y =  -1.0f;
+    segments[0].point3.x =   0.0f;
+    segments[0].point3.y =  -1.0f;
+
+    segments[1].point1.x =  coeff;
+    segments[1].point1.y =  -1.0f;
+    segments[1].point2.x =   1.0f;
+    segments[1].point2.y = -coeff;
+    segments[1].point3.x =   1.0f;
+    segments[1].point3.y =   0.0f;
+
+    segments[2].point1.x =  1.0f;
+    segments[2].point1.y = coeff;
+    segments[2].point2.x = coeff;
+    segments[2].point2.y =  1.0f;
+    segments[2].point3.x =  0.0f;
+    segments[2].point3.y =  1.0f;
+
+    segments[3].point1.x = -coeff;
+    segments[3].point1.y =   1.0f;
+    segments[3].point2.x =  -1.0f;
+    segments[3].point2.y =  coeff;
+    segments[3].point3 = start_point;
+
+    m._11 = ellipse->radiusX;
+    m._12 = 0.0f;
+    m._21 = 0.0f;
+    m._22 = ellipse->radiusY;
+    m._31 = ellipse->point.x;
+    m._32 = ellipse->point.y;
+
+    d2d_point_transform(&start_point, &m, start_point.x, start_point.y);
+    for (i = 0; i < ARRAY_SIZE(segments); ++i)
+    {
+        d2d_point_transform(&segments[i].point1, &m, segments[i].point1.x, segments[i].point1.y);
+        d2d_point_transform(&segments[i].point2, &m, segments[i].point2.x, segments[i].point2.y);
+        d2d_point_transform(&segments[i].point3, &m, segments[i].point3.x, segments[i].point3.y);
+    }
+
+    if (!d2d_figure_begin(&figure, start_point, D2D1_FIGURE_BEGIN_FILLED))
+        return E_OUTOFMEMORY;
+    if (!d2d_figure_add_beziers(&figure, segments, ARRAY_SIZE(segments)))
+    {
+        d2d_figure_cleanup(&figure);
+        return E_OUTOFMEMORY;
+    }
+    d2d_figure_end(&figure, D2D1_FIGURE_END_CLOSED);
+
+    d2d_figure_simplify(&figure, option, transform, tolerance, sink);
+    d2d_figure_cleanup(&figure);
+
+    return S_OK;
 }

static HRESULT STDMETHODCALLTYPE d2d_ellipse_geometry_Tessellate(ID2D1EllipseGeometry *iface,