Custom decorative articles and system, apparatus, and method for providing the same

A non-transitory computer-readable-medium comprising instructions for determining an edge profile of an article to be installed in an installation area, wherein the installation area has a perimeter having a plurality of corners, wherein the instructions of the non-transitory computer-readable-medium, when executed by a computing device, cause the computing device to perform operations comprising:

• receiving data indicative of a plurality of coordinates corresponding to the plurality of corners of the perimeter of the installation area, the plurality of coordinates comprising at least first, second, and third coordinates respectively corresponding to first, second, and third corners of the plurality of corners of the perimeter of the installation area, wherein the second corner is positioned between the first and third coordinates along the perimeter of the installation area;
• determining, based on at least the first, second and third coordinates, dimensional and/or geometric characteristics of a pair of opposed portions of the edge profile that, in an installed position in the installation area, are configured to meet to form a corner of the article when installed at the second corner of the perimeter of the installation area,
• wherein determining, based on at least the first, second and third coordinates, dimensional and/or geometric characteristics of a pair of opposed portions of the edge profile comprises:
• determining a first vector parallel to a line between the first and second coordinates;
• determining a second vector parallel to a line between the second and third coordinates;
• and
• determining an angle between the first and second vectors, and
• wherein determining the dimensional and/or geometric characteristics of opposed portions of the edge profile comprises determining the dimensional and/or geometric characteristics of opposed portions of the edge profile based on the angle between the first and second vectors.

A non-transitory computer-readable-medium comprising instructions for determining an edge profile of an article to be installed in an installation area, wherein the installation area has a perimeter having a plurality of corners, wherein the instructions of the non-transitory computer-readable-medium, when executed by a computing device, cause the computing device to perform operations comprising:

• determining, based on at least the plurality of coordinates corresponding to the plurality of corners of the perimeter of the installation area, dimensional and/or geometric characteristics of respective pairs of opposed portions of the edge profile that, in an installed position in the installation area, are configured to meet to form respective corners of the article when installed at each other corner of the perimeter of the installation area;
• and
• determining portions of the edge profile that, in an installed configuration of the article, correspond to linear segments that extend between ends of adjacent pairs of opposed portions of the edge profile of sequential corners of the article, wherein the pair of opposed portions of the edge profile of each corner of the article and the linear segments cooperate to define an entirety of the edge profile of the article;
• determining, based on the plurality of coordinates corresponding to corners of the perimeter of the installation area, that a standard dimension of a source material cannot provide sufficient material to form the entirety of the edge profile of the article;
• responsive to determining that the standard dimension of the source material cannot provide sufficient material to form the entirety of the edge profile of the article, distributing the edge profile of the article between at least a first article segment from a first source material and a second article segment from a second source material, wherein the first and second article segments meet at a linear intersection and define respective portions of the edge profile of the article.

A non-transitory computer-readable-medium comprising instructions for determining an edge profile of an article to be installed in an installation area, wherein the installation area has a perimeter having a plurality of corners, wherein the instructions of the non-transitory computer-readable-medium, when executed by a computing device, cause the computing device to perform operations comprising:

• receiving data indicative of a plurality of coordinates corresponding to the plurality of corners of the perimeter of the installation area, the plurality of coordinates comprising at least first, second, and third coordinates respectively corresponding to first, second, and third corners of the plurality of corners of the perimeter of the installation area, wherein the second corner is positioned between the first and third coordinates along the perimeter of the installation area;
• determining, based on at least the first, second and third coordinates, dimensional and/or geometric characteristics of a pair of opposed portions of the edge profile that, in an installed position in the installation area, are configured to meet to form a corner of the article when installed at the second corner of the perimeter of the installation area;
• determining a plurality of miter vectors corresponding to respective corners of the perimeter of the installation area,
• wherein each miter vector of the plurality of miter vectors has an angle that bisects the pair of opposed portions of the edge profile, and
• wherein determining the dimensional and/or geometric characteristics of opposed portions of the edge profile comprises mirroring respective traces across a respective miter vector of the plurality of vectors to define the pair of opposed portions of the edge profile.

A non-transitory computer-readable-medium comprising instructions for determining an edge profile of an article to be installed in an installation area, wherein the installation area has a perimeter having a plurality of corners, wherein the instructions of the non-transitory computer-readable-medium, when executed by a computing device, cause the computing device to perform operations comprising:

• receiving data indicative of a plurality of coordinates corresponding to the plurality of corners of the perimeter of the installation area, the plurality of coordinates comprising at least first, second, and third coordinates respectively corresponding to first, second, and third corners of the plurality of corners of the perimeter of the installation area, wherein the second corner is positioned between the first and third coordinates along the perimeter of the installation area;
• and
• determining, based on at least the first, second and third coordinates, dimensional and/or geometric characteristics of a pair of opposed portions of the edge profile that, in an installed position in the installation area, are configured to meet to form a corner of the article when installed at the second corner of the perimeter of the installation area,
• wherein the opposed portions of the pair of opposed portions of the edge profile each comprise an arcuate sub-portion and a straight sub-portion.