Mechanical geometry theorem proving
Mechanical geometry theorem proving
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Emulating the human interpretation of line-drawings as three-dimensional objects
International Journal of Computer Vision
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Computing rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
A Graph-Based Method for Face Identification from a Single 2D Line Drawing
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Transforming an under-constrained geometric constraint problem into a well-constrained one
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Numerical Methods for Beautification of Reverse Engineered Geometric Models
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
On the Numerical Redundancies of Geometric Constraint Systems
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Constraint solving for computer-aided design
Constraint solving for computer-aided design
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Algorithms for identifying rigid subsystems in geometric constraint systems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
A constraint solver to define correctly dimensioned and overdimensioned parts
Computer-Aided Design
Towards beautification of freehand sketches using suggestions
Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
Using sketches and retrieval to create LEGO models
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
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3D models reconstructed from 2D sketches are inaccurate because of the inherent inaccuracies in the input and the reconstruction method. It is therefore necessary to ''beautify'' them before use in CAD systems. We present a method that detects geometric constraints, such as parallel and orthogonal faces, present in the reconstructed model and then selects a subset that constrains the object sufficiently and consistently. The subset selection algorithm first prioritizes the constraints depending on their type and then uses a novel method, based on quasi-Newton optimization, to detect and eliminate redundant and inconsistent constraints. The remaining constraints then define the dimensions of the model fully and consistently. Results from our implementation show that the method can beautify and dimension recovered 3D models correctly at acceptable speed.