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(b) FIGURE 1. First and Second Order approximation of tensor-splatting. (a) Tensors assumed to be non-overlapping and tensor-splat is a tex- ture map positioned at a depth given by its centroid, pz. Textures then mapped in front-to-back order. (b) Tensor-splatting admitting a single overlap between tensors ellipsoids. Now the tensor-splats have to be split into single and double integrals according to the overlap in x and z . In the example, 5 texture maps are required: f(x0; x2)£(z0; z1)g;f(x1; x2)£(z0; z1)g;f(x1; x2)£(z1; z2)g;f(x1; x2)£ (z2; z3)g;f(x2; x3)£(z2; z3)g . (a) (b) (c) (d) FIGURE 2. Tensor-splatting 50 randomly coloured tensors arranged in a spiral. (a) Principal axes of Gaussian footprints overlayed on result. (b) Gaussian modulated opacity maps replaced by a chess-board pat- tern to illustrate the texture mapping and compositing. (c) Spiral with- out shading. (d) Spiral with shading using the lit-tensor Phong shading model.

Tensor Splats: Visualising Tensor Fields by Texture Mapped Volume Rendering