### Description

GANITH is an algebraic geometry tookit, used for the computation and visualization of algebraic equations. It also provides the computational mathematics infrastructure for the Shastra toolkits.

### Usages

Example applications of this for geometric modeling and computer graphics are algebraic curve and surface display, curve-curve intersections, surface-surface intersections, global and local parameterizations, implicitization. GANITH also incorporates techniques for interpolation and least-squares approximation (multivariate data fitting) with algebraic curves and surfaces. The GANITH algebraic geometry toolkit manipulates arbitrary degree polynomials and power series.e It can be used to solve a system of algebraic equations Power series manipulations are used to generate piecewise rational pproximations to algebraic curves and surfaces. Arbitrary rational parametric surfaces can be displayed in GANITH, taking care of poles and base points. Animation facilities allow the visualization of entire families of algebraic curves and surfaces.

### Download

Download information is here.

### Software Usage

### References

C. Bajaj, A. Royappa

**The GANITH Algebraic Geometry Toolkit**

_Proceedings: 1st Annual Conference on the Design and Implementation of Symbolic Computation Systems, Lecture Notes in Computer Science, No. 429, Springer-Verlag, (1990), 268-269.__

S. Abhyankar, C. Bajaj

**Automatic Parameterization of Rational Curves and Surfaces I: Conics and Conicoids**

*Computer Aided Design, 19, 1, (1987), 11-14.* (pdf)

S. Abhyankar, C. Bajaj

**Automatic Parameterization of Rational Curves and Surfaces II: Cubics and Cubicoids**

*Computer Aided Design, 19, 9, (1987), 499-502.* (pdf)

S. Abhyankar, C. Bajaj

**Automatic Parameterization of Rational Curves and Surfaces III: Algebraic Plane Curves**

*Computer Aided Geometric Design, 5:4(1988), 309-321.* (pdf)

C. Bajaj, C. Hoffmann, R. Lynch, J. Hopcroft

**Tracing Surface Intersections**

*Computer Aided Geometric Design, 5:4(1988), 285-307.* (pdf)

S. Abhyankar, C. Bajaj

**Automatic Parameterization of Rational Curves and Surfaces IV: Algebraic Space Curves**

*ACM Transactions on Graphics, 8, 4, (1989), 325-334.* (pdf)

C. Bajaj, G. Xu

**NURBS Approximation of Surface/Surface Intersection Curves**

*Advances in Computational Mathematics, 2, 1, (1994), 1-21.*

C. Bajaj, G. Xu

**Piecewise Rational Approximation of Real Algebraic Curves**

*Journal of Computational Mathematics, vol. 15, no. 1, (1997), 55-71.*

C. Bajaj, G. Xu

**Spline Approximations of Real Algebraic Surfaces**

*Journal of Symbolic Computation, Special Isssue on Parametric Algebraic Curves and Applications, 23, 2-3, (1997), 315 - 333.* (pdf)

C. Bajaj, R. Holt, A. Netravali

**Rational Parameterizations of Nonsingular Real Cubic Surfaces**

*ACM Transactions on Graphics, 17, 1, (1998), 1-31* (pdf)

C. Bajaj, A. Royappa

**Parameterization in Finite Precision**

*Proceedings: Graphics Interface '92, (1992), Vancouver, Canada, Canadian Information Processing Society, 29-36.*

C. Bajaj, G. Xu

**Rational Spline Approximations of Real Algebraic Curves and Surfaces**

*Advances in Computational Mathematics, edited by H.P. Dikshit and C. Michelli, World Scientific Publishing Co., Approximations and Decomposition Series, vol 4., (1994), 73-85.*

C. Bajaj

**Geometric Computations with Algebraic Varieties of Bounded Degree**

*Proceedings: 6th Annual ACM Symposium on Computational Geometry, (1990) Berkeley, California, 148-156.* (pdf)