When I first proposed adding meshes to the SVG standard the SVG working group looked at the question of Coons patch vs tensor patch meshes. A tensor patch adds four additional control points to a Coons patch. These control points influence how the color is spread inside the patch. The group decided that the added complexity of the tensor patch was not worth the benefit gain. I am now revisiting this decision. In a previous blog I discussed the problems caused by a lack of smoothness across patch boundaries. At first it didn’t seem like having tensor control points would help but now I realize that in some limited cases they can be of great benefit.
Consider the following four patch mesh:
The first thing that one sees is a cross pattern. This is due to a lack of smoothness across the patch boundaries. In the following figure one can see the color profile for two of the patches that clearly illustrates the sharp change in the color derivative at the patch boundary.
By moving the tensor mesh points it is possible to better approximate a rotationally symmetric profile around the center point, reducing the “cross” artifact.
It is not possible to completely remove the cross using tensor control points. One also still has a bright spot at the center point which is not what one wants when trying to illustrate a diffuse reflection of light off a curved surface. To get a smoother profile one needs to add more patches.
So adding tensor control points is useful but is not a complete solution to smoothness. I still haven’t made up my mind about their cost/benefit value. Feedback would be appreciated.
