Nonlinear Vector Graphs for Complex Geometries
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Solution Overview
Problem
Conventional vector object representations rely on linear paths, which are inadequate for accurately depicting complex geometries and junctions, leading to inaccuracies and inefficiencies in rendering and editing, especially when approximating shapes like circles, and require holistic reordering of path segments for edits.
Innovation Solution
The implementation of nonlinear vector graphs that use a variety of primitives, including line, cubic Bézier, circular arc, and conic primitives, with explicit indexing of points and primitives, allowing for accurate representation of complex geometries and junctions without approximation inaccuracies and enabling efficient edits by modifying the structure and properties of the vector object without reordering.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional linear path representations are used, then the representation is simple and easy to implement, but the accuracy of complex geometries and junctions deteriorates
Solution Approach 1:
The vector path is segmented into multiple types of primitives (line segments, cubic Bézier curves, circular arcs, conic sections) rather than using a single uniform representation. Each primitive type is selected based on the specific geometric requirements of that segment, allowing accurate representation of complex geometries while maintaining manageable complexity through modular segmentation.
Solution Approach 2:
The patent introduces curved primitives (circular arcs and conic sections) to accurately represent curved geometries without approximation. This replaces the conventional approach of using only straight lines and cubic Bézier curves, enabling precise representation of circles, ellipses, and other curved shapes with their native geometric forms.
2Productivity
If linear path representations are used, then the structure is simple, but editing efficiency deteriorates due to required holistic reordering
Solution Approach 1:
The path is divided into independent primitive segments that can be individually identified and manipulated. Each primitive is a self-contained unit with defined start and end points, allowing editors to modify specific segments without affecting the entire path structure or requiring reordering of other segments.
Solution Approach 2:
The patent transitions from a one-dimensional linear sequence of path points to a two-dimensional structured representation where primitives are organized in a graph-like structure with explicit connections. This dimensional change allows for more flexible editing operations where primitives can be added, removed, or modified without requiring sequential reordering of the entire path.
3Reliability
If conventional approximation methods are used, then the representation is computationally efficient, but visual quality deteriorates
Solution Approach 1:
The patent uses native curved primitives (circular arcs for circles, conic sections for ellipses) to represent curved geometries exactly rather than approximating them with cubic Bézier curves. This eliminates visual artifacts and maintains geometric integrity, particularly important for technical drawings and precise graphic design where circular and elliptical shapes must maintain their true form.
Solution Approach 2:
The patent introduces additional parameters for each primitive type (radius and center for circular arcs, focal points and axes for conic sections) that precisely define the geometry. These parameters allow for exact mathematical representation of curves, replacing the approximate parameter control points used in cubic Bézier curves, thereby improving visual fidelity while maintaining computational manageability through well-defined parametric equations.
Data Source
AI summary
Techniques for nonlinear representations for vector objects are described that support construction of a nonlinear vector graph to represent a vector object. In an implementation, a user input is received including a plurality of points and at least one primitive. A content processing system then generates a vector object by constructing a nonlinear vector graph that specifies a nonlinear connection of the plurality of points with the at least one primitive. In some examples, the vector object is edited by applying an edit to the nonlinear vector graph. Once generated, the content processing system then outputs the vector object for display, e.g., in a user interface.