Triangle Mesh Generation from Curves via Barycentric Binding
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Solution Overview
Problem
Existing methods for generating triangle meshes from images represented by curves, such as those using the convex hull or curve sampling, fail to accurately connect image components, result in overly complex meshes, and do not account for regions obscured by clipping paths, leading to unsatisfactory results in graphics workflows.
Innovation Solution
The technique involves rasterizing an image, generating an outline, reducing it to connected polylines, and creating a triangle mesh from these polylines, decoupling mesh density from curve density, and binding curve samples to the mesh using barycentric coordinates to include obscured regions, allowing for deformation and reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If the convex hull of a tightest polygon is used to generate a triangle mesh, then the mesh covers the entire image, but the mesh includes regions not represented by the artwork and connects components that were not originally connected
Solution Approach 1:
The patent extracts only the necessary regions for mesh generation by using curve sampling to identify actual artwork boundaries, then generates the mesh only within those boundaries using a polygon triangulation algorithm, excluding regions not represented by the artwork
Solution Approach 2:
The patent segments the image into multiple independent mesh regions based on disconnected curve components, allowing each component to have its own mesh that accurately represents only its corresponding artwork portion without connecting unrelated components
2Manufacturing precision
If curve sampling is used to generate a triangle mesh, then the mesh accurately represents the image components, but the mesh density is coupled to curve density resulting in prohibitively large numbers of triangles
Solution Approach 1:
The patent applies local quality by using curve sampling only to determine boundary definitions and vertex positions, then generates triangles with uniform or controlled density within each polygon, decoupling the mesh density from the curve complexity while maintaining accuracy at critical boundaries
Solution Approach 2:
The patent performs preliminary curve sampling to extract essential geometric information (vertices and boundaries) before mesh generation, using this extracted information to define polygons that are then triangulated with a controlled number of triangles independent of the original curve complexity
3Productivity
If traditional methods are used to generate a triangle mesh, then the mesh is generated from visible curves, but regions obscured by clipping paths are not accounted for during deformation
Solution Approach 1:
The patent performs preliminary sampling of curves including those obscured by clipping paths before mesh generation, storing this information to guide mesh deformation in a way that accounts for the presence and position of clipping paths, ensuring accurate reconstruction of both visible and obscured regions
Data Source
AI summary
Systems and techniques are described herein for generating a triangle mesh for an image represented by curves (e.g., Bezier segments). An outline of an image is determined and reduced to a set of connected polylines that are efficiently represented in an edge list. A triangle mesh is generated based on the edge list, rather than by directly sampling the curves of the image and using the samples as vertices of triangles. Thus, the triangle mesh is generated with a number of triangles independent from a number of curves representing the image. Samples of the curves are bound to the triangle mesh by representing the samples with barycentric coordinates with respect to a triangle in the mesh. Hence, once a mesh is deformed, locations of the samples are determined from the barycentric coordinates and triangles in the deformed mesh, and used to reconstruct the curves of the deformed image.