Triangle Generation Apparatus for Equilateral Shape Correction
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Solution Overview
Problem
Existing methods for dividing triangles in computer graphics often result in subdivided triangles that are less like equilateral triangles, leading to decreased analysis accuracy and increased calculation time.
Innovation Solution
A triangle generation apparatus that includes an acquisition unit and a triangle division unit. The triangle division unit determines whether each basic triangle is a target triangle similar to an equilateral triangle and divides non-target triangles into multiple triangles to enhance their similarity to equilateral triangles, thereby maintaining the accuracy of analysis and reducing calculation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional triangle division methods are used, then the triangle can be divided into smaller parts, but the subdivided triangles lose similarity to equilateral triangles, decreasing analysis accuracy
Solution Approach 1:
The patent applies preliminary action by performing a shape correction process before the actual triangle division. The correction unit adjusts the shape of the triangle to be more similar to an equilateral triangle before dividing it into subdivided triangles. This preliminary shape adjustment ensures that the resulting subdivided triangles maintain higher similarity to equilateral triangles, thereby preserving analysis accuracy while still achieving the desired subdivision.
2Productivity
If traditional triangle division methods are used, then the triangle can be divided into smaller parts, but the calculation time increases
Solution Approach 1:
By performing shape correction before division, the patent creates triangles that are more suitable for efficient processing. The corrected triangles with shapes closer to equilateral triangles require fewer iterative calculations and converge faster in subsequent analysis operations, thereby reducing overall calculation time despite adding a preliminary correction step.
Solution Approach 2:
The patent changes the shape parameters of the triangle (adjusting angles and side lengths) to move closer to the ideal equilateral triangle configuration before division. This parameter optimization ensures that the subdivided triangles have more favorable geometric properties for numerical analysis, improving computational efficiency and reducing calculation time.
3Device complexity
If the triangle shape is not corrected before division, then the process is simpler, but the subdivided triangles have poor geometric properties
Solution Approach 1:
The patent introduces a preliminary shape correction step that adjusts the triangle's geometry before division. This additional step, while increasing process complexity, ensures that the subdivided triangles have superior geometric properties (closer to equilateral shapes), which are critical for maintaining numerical stability and accuracy in subsequent analysis operations.
Data Source
AI summary
A triangle generation apparatus includes an acquisition unit and a triangle division unit. The acquisition unit acquires a vertex coordinate group including coordinates of each vertex of one or a plurality of basic triangles. The triangle division unit divides each basic triangle defined by the coordinates of the vertices included in the vertex coordinate group into a plurality of subdivided triangles. The triangle division unit determines whether each basic triangle defined by the vertex coordinate group is a target triangle that has a shape having a relatively high degree of similarity to an equilateral triangle. The triangle division unit divides the basic triangle determined to not be the target triangle into a plurality of triangles to have the shape having a relatively high degree of similarity to an equilateral triangle. The triangle division unit generates the new vertex coordinate group including the vertex coordinates of the triangles after division.