PAINT REFLECTION AROUND A CURVILINEAR PATH
Techniques for creating a mirror symmetric image using a curvilinear or non-linear axis of symmetry (symmetry axis) in 2-D or 3-D space. For each of a set of sample points defining an image, a respective tangent line associated with a sample point is determined with respect to the curvilinear axis of symmetry. A linear paint reflection operation is then performed with respect to the current sample point and the respective tangent line to generate a respective symmetry point. The operation is performed for each sample point such that an aggregate reflection is performed for all sample points to generate a reflected image around the curvilinear path.
1 . A method for performing paint reflection of a plurality of sample points around a curvilinear path, the method comprising:
receiving a curvilinear path, wherein said curvilinear path comprises a plurality of points and separates a first region from a second region;
for a sample point within said first region, determining an associated reflected point in said second region by:
determining a closest point on said curvilinear path contour; and,
performing a linear paint reflection operation with respect to said sample point and said closest point to generate said associated reflected point.
2 . The method according to claim 1 , wherein performing a linear paint reflection comprises:
computing a perpendicular from said sample point to said closest point; and,
generating a reflected perpendicular from said perpendicular to generate said reflected point, wherein said reflected point comprises an endpoint of said reflected perpendicular.
3 . The method according to claim 2 , wherein computing a perpendicular further comprises:
determining a tangent line at said closest point; and,
determining said a perpendicular line to said tangent line.
4 . The method according to claim 1 , wherein said plurality of sample points and said curvilinear path are generated based on input received from a digital input device.
5 . The method according to claim 1 , wherein said curvilinear path is extended beyond an endpoint associated with such curvilinear path by concatenating a straight line at said endpoint, said straight line having a slope associated with a point near said endpoint.
6 . The method according to claim 1 , wherein said sample points lie in a 2D space.
7 . The method according to claim 1 , wherein said sample points lie in a 3D space.
8 . A system for performing paint reflection of a plurality of sample points around a curvilinear path comprising:
a processor, wherein said processor is adapted to execute a curvilinear paint reflection process, said process further comprising:
receiving a curvilinear path, wherein said curvilinear path comprises a plurality of points and separates a first region from a second region;
for a sample point within said first region, determining an associated reflected point in said second region by:
determining a closest point on said curvilinear path contour; and,
performing a linear paint reflection operation with respect to said sample point and said closest point to generate said associated reflected point.
9 . The system according to claim 8 , wherein performing a linear paint reflection further comprises:
computing a perpendicular from said sample point to said closest point; and,
generating a reflected perpendicular from said perpendicular to generate said reflected point, wherein said reflected point comprises an endpoint of said reflected perpendicular.
10 . The system according to claim 8 , wherein said plurality of sample points and said curvilinear path are generated from a digital input device.
11 . The system according to claim 8 , wherein said curvilinear path is extended beyond an endpoint associated with such curvilinear path by concatenating a straight line at said endpoint, said straight line having a slope associated with a point near said endpoint.
12 . The system according to claim 9 , wherein computing a perpendicular further comprises:
determining a tangent line at said closest point; and,
determining said a perpendicular line to said tangent line.
13 . The system according to claim 8 , wherein said sample points lie in a 2D plane.
14 . The system according to claim 8 , wherein said sample points lie in a 3D space.
15 . A computer program product including one or more non-transitory machine-readable mediums encoded with instructions that when executed by one or more processors cause a process to be carried out for performing paint reflection of a plurality of sample points around a curvilinear path, the method comprising:
receiving a curvilinear path, wherein said curvilinear path comprises a plurality of points, and separates a first region from a second region;
for a sample point within said first region, determining an associated reflected point in said second region by:
determining a closest point on said curvilinear path contour; and,
performing a linear paint reflection operation with respect to said sample point and said closest point to generate said associated reflected point.
16 . The computer program product according to claim 15 , wherein performing a linear paint reflection further comprises:
computing a perpendicular from said sample point to said closest point; and,
generating a reflected perpendicular from said perpendicular to generate said reflected point, wherein said reflected point comprises an endpoint of said reflected perpendicular.
17 . The computer program product according to claim 15 , wherein said plurality of sample points and said curvilinear path are generated from a digital input device.
18 . The computer program product according to claim 15 , wherein said curvilinear path is extended beyond an endpoint associated with such curvilinear path by concatenating a straight line at said endpoint, said straight line having a slope associated with a point near said endpoint.
19 . The computer program product according to claim 16 , wherein generating a perpendicular further comprises:
determining a tangent line at said closest point; and,
determining said a perpendicular line to said tangent line.
20 . The computer program product according to claim 15 , wherein said sample points lie in a 2D plane.