On the algebraic and geometric foundations of computer graphics
ACM Transactions on Graphics (TOG)
Vector Geometry for Computer Graphics
IEEE Computer Graphics and Applications
The Ambient Spaces of Computer Graphics and Geometric Modeling
IEEE Computer Graphics and Applications
Modeling 3D Euclidean Geometry
IEEE Computer Graphics and Applications
Computer Graphics in its Fifth Decade: Ferment at the Foundations
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Quality metrics for geologic grid structures
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra: A Powerful Tool for Solving Geometric Problems in Visual Computing
SIBGRAPI-TUTORIALS '09 Proceedings of the 2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
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In vector geometry there are 2 distinct types of entities: points P, Q, R … and vectors u, v, w … Generally, the operattions of vector algebra —addition, subtraction, scalar multiplication, dot product, and cross product—are intrinsically defined only for vectors, not for points. Yet illicit expressions containing terms like P + Q, cP, P X Q, etc. often appear in graphics textbooks, papers, and programs. In this paper we justify the use of such illicit expressions, and we we give criteria for recognizing when such an expression is truly legitimate. In particular we show that an algebraic expression E(P1, …, Pn) is legitimate if and onl y if E(v1 + w, …vn + w) = E(v1, …, vn) + kw, k + 0, 1. We also derive many useful examples of such an expression.