Directed Acyclic Graph Constraint Evaluation for 3D Objects
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Solution Overview
Problem
As animated media productions become more complex, the manual manipulation of multiple virtual 3D objects to create realistic interactions is cumbersome and time-consuming, especially when trying to depict one object being manipulated by another, as existing graph-based systems lack efficient methods for constraining objects without causing cyclic dependencies and incompatibilities.
Innovation Solution
A method using directed acyclic graphs (DAGs) to constrain virtual 3D objects by establishing parent-child relationships, ensuring compatibility, and evaluating constraint relationships to render images effectively, allowing objects to move, rotate, and scale together while avoiding cyclic constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If manual manipulation of multiple virtual 3D objects is used to create realistic interactions, then animation realism is improved, but animation efficiency and time consumption deteriorate
Solution Approach 1:
The patent replaces manual mechanical manipulation of virtual objects with an automated constraint-based system. Instead of animators manually positioning objects frame-by-frame, the system uses constraint graphs with mathematical formulations to automatically calculate and enforce spatial relationships between objects, substituting human manual operations with automated computational mechanics.
Solution Approach 2:
The patent changes the parameter representation from individual object transformations to constraint relationship parameters. By defining relationships through constraint types (e.g., parent-child, sibling) and mathematical parameters (weights, offsets, transformation matrices), the system enables automated computation of object positions based on relationship parameters rather than manual position specification.
2Reliability
If constraint relationships are established between virtual 3D objects, then object interaction realism is improved, but system complexity increases
Solution Approach 1:
The patent segments the constraint system into distinct modular components: constraint nodes representing virtual objects, constraint edges representing relationships, and evaluation modules processing specific constraint types. This segmentation allows complex interactions to be broken down into manageable, independently evaluable units that can be composed to achieve realistic object interactions.
Solution Approach 2:
The patent introduces constraint graphs as intermediary structures between objects. Instead of direct object-to-object manipulation, objects interact through the mediator constraint system that enforces spatial relationships. The constraint graph serves as an intermediary layer that manages complexity by abstracting direct interactions into relationship definitions.
3Ease of operation
If graph-based systems are used to represent virtual objects and their relationships, then object relationship management is improved, but cyclic dependency issues arise
Solution Approach 1:
The patent implements dynamic constraint evaluation that adapts to the constraint graph structure. The system dynamically determines evaluation order based on dependency relationships, using algorithms that detect and handle cyclic dependencies by identifying cycles and breaking them through iterative relaxation or topological sorting, allowing flexible relationship management while maintaining reliability.
Solution Approach 2:
The patent incorporates feedback mechanisms in constraint evaluation where the system continuously monitors constraint satisfaction and adjusts object positions iteratively. When cyclic dependencies are detected, the feedback loop identifies the conflict and triggers resolution protocols such as relaxing certain constraints or reordering evaluation, ensuring reliable constraint management.
Data Source
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AI summary
Systems and processes are described below relating to evaluating a dependency graph to render three-dimensional (3D) graphics using constraints. Two virtual 3D objects are accessed in a virtual 3D space. A constraint relationship request is received, which identifies the first object as a parent and the second object as a child. The technique verifies whether the graphs of the objects are compatible for being constrained to one another. The first object is evaluated to determine its translation, rotation, and scale. The second object is similarly evaluated based on the translation, rotation, and scale of the first object. An image is rendered depicting at least a portion of the first virtual 3D object and at least a portion of the second virtual 3D object.