The systems and methods described herein may allow diffusion curve images to be displayed by a variety of applications without requiring specialized graphics hardware to render the images. The system may provide mechanisms to convert a diffusion curve representation to an alternate representation in a scalable, portable format. The conversion may include a tessellation operation, and may produce a mesh of shapes (e.g., triangles) for which diffusible attribute values (e.g. color and blur) are assigned to each node. Tessellating an image may include generating a piecewise linear approximation of the diffusion curves and triangulating the image to generate the mesh. Color values for each channel may be assigned by solving a sparse linear system in the triangle domain. The alternate representation may be displayed by another application using various interpolation techniques. The alternate representation may be resolution-independent and compact, as compared to other representations used to display diffusion curve images.