Streamlined tetrahedral interpolation

A method for obtaining plural output color component values representing an output color in an output color format from plural input color component values representing an input color in an input color format, the method comprising the steps of:

• constructing a cubic grid, each axis of the cubic grid corresponding to a type of input color component value, and each vertex of the cubic grid corresponding to plural output color component value entries;
• determining an entry in the cubic grid corresponding to a vertex of a cube which includes the input color, the cube comprising plural tetrahedrons;
• calculating plural weights based on distances of the plural input color component values from at least one vertex of the cube;
• storing the plural weights in a look-up table accessible by an index;
• calculating the index, the index indicating which of the plural tetrahedrons of the cube corresponds to the plural input color component values;
• accessing the plural weights corresponding to the index in the look-up table;
• and
• applying the accessed plural weights to plural output color component value entries corresponding to vertices that form the indicated tetrahedron of the cube so as to obtain the plural output color component values corresponding to the output color,
• wherein the step of calculating the index consists of a fixed set of assembler instructions, all of which are performed regardless of relative values of the input color component values.

An apparatus for obtaining an interpolated color output value corresponding to a color input value based on a color look-up table which stores color output values of each vertex of a cubic grid of color input values, comprising:

• a memory including a region for storing the color look-up table, a region for storing a temporary look-up table, and a region for storing executable process steps;
• and
• a processor for executing the executable process steps;
• wherein the executable process steps include steps of:
• (a) calculating plural weights for the color input value, each of the plural weights depending on color component values that together constitute the color input value, each of the weights corresponding to respective ones of plural tetrahedrons into which each cube of the cubic grid is dissected;
• (b) storing the calculated weights in the temporary look-up table accessible by an index;
• (c) executing a block of code to calculate the index, the block of code not including conditional branch instructions conditioned on a comparison of the plural component values of the color input value, the index being based on relative magnitude of the component values of the color input value;
• and (d) applying weights at the indexed location of the temporary look-up table to the color output values in the color look-up table so as to obtain an interpolated color output value corresponding to the color input value.

An apparatus for obtaining plural output color component values representing an output color in an output color format from plural input color component values representing an input color in an input color format, comprising:

• a memory including a region for storing color component values and a region for storing executable process steps;
• and
• a processor for executing the executable process steps;
• wherein the executable process steps include steps of:
• (a) constructing a cubic grid, each axis of the cubic grid corresponding to a type of input color component value, and each vertex of the cubic grid corresponding to plural output color component value entries;
• (b) determining an entry in the cubic grid corresponding to a vertex of a cube which includes the input color, the cube comprising plural tetrahedrons;
• (c) calculating plural weights based on distances of the plural input color component values from at least one vertex of the cube;
• (d) storing the plural weights in a look-up table accessible by an index;
• (e) calculating the index, the index indicating which of the plural tetrahedrons of the cube corresponds to the plural input color component values, the step of calculating the index consisting of a fixed set of assembler instructions, all of which are performed regardless of relative values of the input color component values;
• (f) accessing the plural weights corresponding to the index in the look-up table;
• and (g) applying the accessed plural weights to plural is output color component value entries corresponding to vertices that form the indicated tetrahedron of the cube so as to obtain the plural output color component values corresponding to the output color.

Computer-executable process steps stored on a computer-readable medium, the computer executable process steps to obtain an interpolated color output value corresponding to a color input value based on a color look-up table which stores color output values of each vertex of a cubic grid of color input values, the computer-executable process steps comprising:

• code to calculate plural weights for the color input value, each of the plural weights depending on color component values that together constitute the color input value, each of the weights corresponding to respective ones of plural tetrahedrons into which each cube of the cubic grid is dissected;
• code to store the calculated weights in a temporary look-up table accessible by an index;
• code to calculate the index, the code to calculate the index not including conditional branch instructions conditioned on a comparison of the plural component values of the color input value, the index being based on relative magnitude of the component values of the color input value;
• and
• code to apply weights at the indexed location of the temporary look-up table to the color output values in the color look-up table so as to obtain an interpolated color output value corresponding to the color input value.

Computer-executable process steps stored on a computer-readable medium, the computer executable process steps to obtain plural output color component values representing an output color in an output color format from plural input color component values representing an input color in an input color format, the computer-executable process steps comprising:

• code to construct a cubic grid, each axis of the cubic grid corresponding to a type of input color component value, and each vertex of the cubic grid corresponding to plural output color component value entries;
• code to determine an entry in the cubic grid corresponding to a vertex of a cube which includes the input color, the cube comprising plural tetrahedrons;
• code to calculate plural weights based on distances of the plural input color component values from at least one vertex of the cube;
• code to store the plural weights in a look-up table accessible by an index;
• code to calculate the index, the index indicating which of the plural tetrahedrons of the cube corresponds to the plural input color component values;
• code to access the plural weights corresponding to the index in the look-up table;
• and
• code to apply the accessed plural weights to plural output color component value entries corresponding to vertices that form the indicated tetrahedron of the cube so as to obtain the plural output color component values corresponding to the output color,
• wherein the code to calculate the index consists of a fixed set of assembler instructions, all of which are performed regardless of relative values of the input color component values.

A computer-readable medium which stores computer-executable process steps, the computer-executable process steps to obtain an interpolated color output value corresponding to a color input value based on a color look-up table which stores color output values of each vertex of a cubic grid of color input values, the computer-executable process steps comprising:

• a calculating step to calculate plural weights for the color input value, each of the plural weights depending on color component values that together constitute the color input value, each of the weights corresponding to respective ones of plural tetrahedrons into which each cube of the cubic grid is dissected;
• a storing step to store the calculated weights in a temporary look-up table accessible by an index;
• an executing step to execute a block of code to calculate the index, the block of code not including conditional branch instructions conditioned on a comparison of the plural component values of the color input value, the index being based on relative magnitude of the component values of the color input value;
• and
• an applying step to apply weights at the indexed location of the temporary look-up table to the color output values in the color look-up table so as to obtain an interpolated color output value corresponding to the color input value.

A computer-readable medium which stores computer-executable process steps, the computer-executable process steps to obtain plural output color component values representing an output color in an output color format from plural input color component values representing an input color in an input color format, the computer-executable process steps comprising:

• a constructing step to construct a cubic grid, each axis of the cubic grid corresponding to a type of input color component value, and each vertex of the cubic grid corresponding to plural output color component value entries;
• a determining step to determine an entry in the cubic grid corresponding to a vertex of a cube which includes the input color, the cube comprising plural tetrahedrons;
• a calculating step to calculate plural weights based on distances of the plural input color component values from at least one vertex of the cube;
• a storing step to store the plural weights in a look-up table accessible by an index;
• a calculating step to calculate the index, the index indicating which of the plural tetrahedrons of the cube corresponds to the plural input color component values;
• an accessing step to access the plural weights corresponding to the index in the look-up table;
• and
• an applying step to apply the accessed plural weights to plural output color component value entries corresponding to vertices that form the indicated tetrahedron of the cube so as to obtain the plural output color component values corresponding to the output color,
• wherein the calculating step to calculate the index consists of a fixed set of assembler instructions, all of which are performed regardless of relative values of the input color component values.