Bibliography
Academic Papers
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Lorensen, W. E., & Cline, H. E. (1987). Marching cubes: A high resolution 3D surface construction algorithm
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Pasko, A., Adzhiev, V., Sourin, A., & Savchenko, V. (1995). Function representation in geometric modeling: concepts, implementation and applications
- Springer • ResearchGate PDF
- Foundational paper for F-rep (Function Representation) modeling, directly relevant to implicit surface work in Crater.rs.
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Rvachev, V. L. (1982). Theory of R-functions and some applications
- Wikipedia • Related PDF
- Theory and applications of R-functions used in CSG operations.
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Ricci, A. (1973). A constructive geometry for computer graphics
- DOI
- Early work on constructive solid geometry for computer graphics.
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Frisken, S. F., Perry, R. N., Rockwood, A. P., & Jones, T. R. (2000). Adaptively sampled distance fields: a general representation of shape for computer graphics
- DOI
- Adaptive distance field representation for efficient shape modeling.
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Appel, A. (1968). Some techniques for shading machine renderings of solids
- ACM DL
- Early work on ray casting and computer graphics rendering.
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Metropolis, N., & Ulam, S. (1949). The Monte Carlo method
- JSTOR
- Introduction to Monte Carlo methods for numerical computation.
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Hart, J. C. (1996). Sphere tracing: A geometric method for the antialiased rendering of implicit surfaces
- Springer
- Sphere tracing algorithm for rendering implicit surfaces.
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Bloomenthal, J., Bajaj, C., Blinn, J., Cani-Gascuel, M. P., Rockwood, A., Wyvill, B., & Wyvill, G. (1997). Introduction to implicit surfaces
- Google Books • Amazon
- Comprehensive introduction to implicit surface modeling and techniques.
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Requicha, A. A. (1980). Representations for rigid solids: Theory, methods, and systems
- ACM DL • Semantic Scholar
- ACM Computing Surveys, 12(4), 437-464 - Foundational work on solid modeling representations.
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Glassner, A. S. (Ed.). (1989). An introduction to ray tracing
- Free PDF • Internet Archive • Amazon
- Morgan Kaufmann - Classic text on ray tracing algorithms and techniques.
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Abramowitz, M., & Stegun, I. A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
- National Bureau of Standards
- Comprehensive reference for special functions, numerical methods, and mathematical formulas.
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Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.)
- Cambridge University Press
- Practical numerical algorithms and computational techniques.
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Boyd, S., & Vandenberghe, L. (2004). Convex Optimization
- Cambridge University Press
- Mathematical foundations of optimization theory and smooth function analysis.