Exemple #1
0
    private static float MaxErrorLocation(ArcOfSphere arc, float begin, float end)
    {
        Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
        Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));

        // 2) use binary / bisection search to find the point of maximal error
        while (end - begin > delta)
        {
            float midpoint = (begin + end) / 2;

            float error_left  = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint - delta)));
            float error_right = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint + delta)));

            if (error_left < error_right) //error begin should be replaced since it has less error
            {
                begin = midpoint;
            }
            else //error end should be replaced since it has less error
            {
                end = midpoint;
            }
        }

        return((begin + end) / 2); // return location of max error
    }
Exemple #2
0
    public static void AddLine(ArcOfSphere edge, float begin, float end)
    {
        Vector2 begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin));
        Vector2 end_UV   = SpaceConverter.SphereToUV(edge.Evaluate(end));

        if (Vector2.Distance(begin_UV, end_UV) > threshold)
        {
            Vector2 delta_begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin + 64 * delta));
            Vector2 delta_end_UV   = SpaceConverter.SphereToUV(edge.Evaluate(end - 64 * delta));
            Vector2 control_point  = Intersection(begin_UV, delta_begin_UV, delta_end_UV, end_UV);

            DebugUtility.Log("AddLine:", begin_UV, end_UV);

            lines.Add(new QuadraticBezier(edge, begin_UV, control_point, end_UV, begin, end));
        }
    }
Exemple #3
0
    private static void Subdivide(ArcOfSphere arc, float begin, float end)
    {
        float midpoint = MaxErrorLocation(arc, begin, end);

        Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
        Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));
        Vector2 P  = SpaceConverter.SphereToUV(arc.Evaluate(midpoint));

        if (Point_Line_Distance(L1, L2, P) > threshold) // if the max error is greater than a threshold, recursively add the left and right halves into the list of lines
        {
            Subdivide(arc, begin, midpoint);
            Subdivide(arc, midpoint, end);
        }
        else
        {
            AddLine(arc, begin, end);
        }
    }