Method of formulating paint through color space modeling

Claim 1

method of determining a paint formulation for producing a paint characterized by desired color coordinates in a three-dimensional color space from a set of known constituents, the method comprising the steps: providing a plurality of color coordinates, each of the color coordinates corresponding to a respective diverse apportionment of the known constituents; performing regression of the color coordinates and the diverse apportionments of the known constituents to establish therefrom a set of interdependent equations having independent variables corresponding to the known constituents and dependent variables corresponding to the color coordinates; providing the desired color coordinates; and, recursively solving the set of interdependent equations for values of the independent variables which substantially equate the dependent variables to the desired color coordinates, whereby the solved values of the independent variables comprise the paint formulation for producing the paint exhibiting the desired color coordinates.

Claim 6

A method of determining a paint formulation for producing a paint characterized by desired color coordinates in a three-dimensional color space from a set of known constituents, the method comprising the steps: providing a number of paint samples, each paint sample characterized by respective diverse constituent apportionment data; producing respective color coordinate data defining, for each paint sample, color position in a three-dimensional color space by a color measuring device; relating the constituent apportionment data to the color coordinate data to derive a formulation model characterized by correlation of the known constituents to color attributes defining color positions in the three-dimensional color space; applying color coordinate data corresponding to the select paint color to the formulation model to determine constituent apportionments corresponding to the select paint color; and, comparing the determined constituent apportionment data to predetermined constituent parameters wherein determined constituent apportionment data comprises the paint formulation for producing the paint exhibiting the desired color coordinates.

Claim 7

A method of determining a paint formulation for producing a paint characterized by desired color coordinates in a three-dimensional color space from a set of known constituents, the method comprising the steps: providing a number of paint samples, each paint sample characterized by respective diverse constituent apportionment data; producing respective color coordinate data defining, for each paint sample, color position in a three-dimensional color space by a color measuring device; relating the constituent apportionment data to the color coordinate data to derive a formulation model characterized by correlation of the known constituents to color attributes defining color positions in the three-dimensional color space; applying color coordinate data corresponding to the select paint color to the formulation model to determine constituent apportionments corresponding to the select paint color; and, comparing the determined constituent apportionment data to predetermined constituent parameters wherein determined constituent apportionment data comprises the paint formulation for producing the paint exhibiting the desired color coordinates.

Claim 8

A method of determining paint formulations for producing paints characterized by color coordinates within a three-dimensional color space common among respective capabilities of a plurality of known paints formulated with respective sets of known constituents, the method comprising the steps: providing for each known paint a plurality of color coordinates, each of the color coordinates corresponding to predetermined diverse apportionments of the respective set of known constituents, said predetermined diverse apportionments having been established in accordance with each respective constituent assuming one of a respective pair of apportionment levels, each respective pair of apportionment levels corresponding to limits of the corresponding constituent affecting the respective capability of the corresponding known paint; performing for each known paint regressions of the corresponding color coordinates and diverse apportionments of the respective set of known constituents to establish therefrom corresponding sets of interdependent equations having independent variables corresponding to the respective known constituents and dependent variables corresponding to the respective color coordinates; providing predetermined color coordinates; and, recursively solving each set of interdependent equations for values of the corresponding independent variables which substantially equate the corresponding dependent variables to the predetermined color coordinates, wherein the solved values for the respective independent variables comprise respective paint formulations for producing paint exhibiting the desired color coordinates, and wherein when each solved value is within the respective limits of the corresponding constituent, the respective paint formulations produce paints characterized by color coordinates within a three-dimensional color space common among respective capabilities of the plurality of known paints.

Claim 9

A method of determining paint formulations for producing paints characterized by color coordinates within a three-dimensional color space common among respective capabilities of a plurality of known paints formulated with respective sets of known constituents, the method comprising the steps: providing for each known paint a plurality of color coordinates, each of the color coordinates corresponding to predetermined diverse apportionments of the respective set of known constituents, said predetermined diverse apportionments having been established in accordance with each respective constituent assuming one of a respective pair of apportionment levels, each respective pair of apportionment levels corresponding to limits of the corresponding constituent affecting the respective capability of the corresponding known paint; performing for each known paint regressions of the corresponding color coordinates and diverse apportionments of the respective set of known constituents to establish therefrom corresponding sets of interdependent equations having independent variables corresponding to the respective known constituents and dependent variables corresponding to the respective color coordinates; providing predetermined color coordinates; and, recursively solving each set of interdependent equations for values of the corresponding independent variables which substantially equate the corresponding dependent variables to the predetermined color coordinates, wherein the solved values for the respective independent variables comprise respective paint formulations for producing paint exhibiting the desired color coordinates, and wherein when each solved value is within the respective limits of the corresponding constituent, the respective paint formulations produce paints characterized by color coordinates within a three-dimensional color space common among respective capabilities of the plurality of known paints.