Triangulating Non-Simple Vector Shapes via Monotone Chains

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Solution Overview

Problem

Existing methods for tessellating vector graphics data are computationally inefficient, unstable, and prone to errors, especially when handling non-simple cases like overlapping edges and shared vertices, leading to issues like 'group opacity' and seam appearance in rendered images.

Innovation Solution

A method involving the creation of monotone chains, scan beams, and computation of monotone polygons to efficiently triangulate multi-styled shapes, which stabilizes the processing of vector graphics data and reduces the number of triangles required, thereby improving computational efficiency and error handling.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If traditional tessellation algorithms are used to convert vector graphics data into triangles, then the display can be achieved, but the computational cost varies greatly depending on image content, making it unsuitable for consistent real-time use

Engineering Contradiction:

Improvetessellation speedVSAvoidcomputational consistency

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The algorithm segments the polygon into monotone chains based on scanline intersections, dividing the complex tessellation problem into simpler sub-problems that can be processed independently and consistently, eliminating content-dependent computational variability

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algorithm performs preliminary actions by pre-processing the polygon into monotone chains and identifying scanline intersections before actual triangulation, ensuring that the computational structure is established in advance for consistent real-time performance

Inventive Principle:

Principle #10Preliminary action

2Productivity

If traditional tessellation algorithms are used, then triangles can be generated, but errors or anomalies in depicting small features can corrupt the displayed image or cause the display device to crash

Engineering Contradiction:

Improvetriangle generation capabilityVSAvoiderror stability

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The algorithm applies beforehand cushioning by using monotone chain decomposition and scanline-based processing that prevents error propagation, cushioning against potential crashes or corruption before they can occur during tessellation

Inventive Principle:

Principle #11Beforehand cushioning (Prior cushioning)

Solution Approach 2:

The algorithm incorporates feedback mechanisms through systematic processing of scanline intersections and monotone chains, where each processing step validates and corrects previous steps, ensuring error-free triangle generation

Inventive Principle:

Principle #23Feedback

3Adaptability or versatility

If multiple layers are rendered with varying opacity using related art approaches, then layered polygons can be displayed, but the 'group opacity' problem occurs when multiple layers are rendered

Engineering Contradiction:

Improvelayered polygon renderingVSAvoidopacity rendering accuracy

Core Design Contradiction:

Adaptability or versatilityVSManufacturing precision

Solution Approach 1:

The algorithm transitions to another dimension by processing polygons in monotone chain order along scanlines, adding a temporal/sequential dimension to the rendering process that resolves opacity conflicts between layers through systematic depth processing

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

4Productivity

If polygons are generated independently in related art approaches, then each polygon can be processed separately, but polygons with shared edges appear with seams between them

Engineering Contradiction:

Improveindependent polygon processingVSAvoidedge alignment accuracy

Core Design Contradiction:

ProductivityVSManufacturing precision

Solution Approach 1:

The algorithm merges adjacent polygons by processing them together through the monotone chain and scanline framework, combining their edge definitions so that shared edges are rendered once and perfectly aligned, eliminating seams while maintaining independent processing efficiency

Inventive Principle:

Principle #5Merging (Combining)

5Adaptability or versatility

If related art approaches are used to handle non-simple cases, then processing can be attempted, but fully or partially overlapped edges, polygon edges passing through vertices, and crossing edges cause processing failures

Engineering Contradiction:

Improvenon-simple case handlingVSAvoidprocessing stability

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The algorithm segments non-simple polygons into monotone chains that systematically handle overlapping edges, vertex intersections, and crossing edges by breaking down complex geometries into manageable segments that can be processed in a defined sequence, ensuring stable processing of non-simple cases

Inventive Principle:

Principle #1Segmentation

Data Source

PatentUS9552670B1System and method for triangulation of non-simple, multiply-connected, multi-styled shapes

Publication Date: 2017.01.24 AUTODESK INC

AI summary

Disclosed is a system and method for triangulating vector graphics data having non-simple multi-styled and multi-connected shapes. The method provides for geometry flattening and more efficient processing of horizontal edges. The method involves computing a plurality of monotone chains corresponding to each of the plurality of shapes; computing a plurality of scan beams corresponding to the plurality of monotone chains; computing a plurality of monotone polygons corresponding to the monotone chains; computing a plurality of triangles from the plurality of monotone polygons; and displaying the plurality of triangles on the computer display.