Method for limiting total colorant coverage using multidimensional simplicial subdivision and barycentric interpolation

A multi-colorant rendering system comprising:

• an output rendering medium having a total area coverage (TAC) limit;
• a rendering mechanism configured to render color on the output rendering medium;
• and
• a processor coupled to the rendering mechanism and configured to:
• define an n-channel colorant space without colorant limitation that may be represented as a first n-dimensional hypercube;
• apply the total area coverage (TAC) limit to the n-channel colorant space to define a legal colorant space, wherein the TAC limit may be represented as an (n−1)-dimensional hyperplane and the legal colorant space may be represented as an irregular polytope;
• and
• apply a bijective transformation between the legal colorant space and a nominal colorant space that may be represented as filling a second n-dimensional hypercube, the bijective transformation being constructed by:
• dividing the nominal colorant space into n-dimensional simplexes;
• finding, for each simplex, intersection points between the TAC limit (n−1)-dimensional hyperplane and the edges of the simplex;
• and
• mapping each simplex of the nominal colorant space onto a corresponding n-dimensional simplex within the legal colorant space using a barycentric interpolation technique.

In a color rendering system, a method for limiting total colorant coverage using multidimensional simplicial subdivision and barycentric interpolation comprising:

• defining an three-channel colorant space without colorant limitation that may be represented as a first three-dimensional cube;
• applying a total area coverage (TAC) constraint to the three-channel colorant space to define a legal colorant space, wherein the TAC constraint may be represented as a two-dimensional plane and the legal colorant space may be represented as an irregular polyhedron;
• and
• applying a bijective transformation between the legal colorant space and a nominal colorant space that may be represented as filling a second three-dimensional cube, the bijective transformation being constructed by:
• dividing the nominal colorant space into tetrahedra;
• finding, for each tetrahedron, intersection points between the TAC constraint plane and the edges of the tetrahedron;
• and
• mapping each tetrahedron of the nominal colorant space onto a corresponding tetrahedron within the legal colorant space using a barycentric interpolation technique.