Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Projective geometry and its applications to computer graphics
Projective geometry and its applications to computer graphics
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
A coordinate-free approach to geometric programming
Theory and practice of geometric modeling
Rational curves and surfaces: applications to CAD
Rational curves and surfaces: applications to CAD
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Illicit expressions in vector algebra
ACM Transactions on Graphics (TOG)
Jim Blinn's corner: a trip down the graphics pipeline
Jim Blinn's corner: a trip down the graphics pipeline
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
A homogeneous formulation for lines in 3 space
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
The Ambient Spaces of Computer Graphics and Geometric Modeling
IEEE Computer Graphics and Applications
Baseball Arithmetic and the Laws of Pseudoperspective
IEEE Computer Graphics and Applications
Clipping using homogeneous coordinates
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Modeling 3D Euclidean Geometry
IEEE Computer Graphics and Applications
Lines in Space: Part 1:The 4D Cross Product
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
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Proceedings of the 20th ACM SIGPLAN workshop on Partial evaluation and program manipulation
Graphical Models
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Today's computer graphics is ostensibly based upon insights from projective geometry and computations on homogeneous coordinates. Paradoxically, however, projective spaces and homogeneous coordinates are incompatible with much of the algebra and a good deal of the geometry currently in actual use in computer graphics. To bridge this gulf between theory and practice, Grassmann spaces are proposed here as an alternative to projective spaces. We establish that unlike projective spaces, Grassmann spaces do support all the algebra and geometry needed for contemporary computer graphics. We then go on to explain how to exploit this algebra and geometry for a variety of applications, both old and new, including the graphics pipeline, shading algorithms, texture maps, and overcrown surfaces.