DISPLAYING QUADRATIC SURFACES ON COMPUTER SCREEN

Deconstructing Functions on Quadratic Surfaces into Multipoles

Any homogeneous polynomial P (x, y, z) of degree d, being restricted to a unit sphere S, admits essentially a unique representation of the form λ + ∑d k=1[ ∏k j=1 Lkj ], where Lkj ’s are linear forms in x, y and z and λ is a real number. The coefficients of these linear forms, viewed as 3D vectors, are called multipole vectors of P . In this paper we consider similar multipole representations o...

The Dirichlet problem on quadratic surfaces

We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in Rn such as ellipsoids, elliptic cylinders, and paraboloids. To produce this algorithm, first we show that every polynomial in Rn can be uniquely written as the sum of a harmonic function and a polynomial multiple of a quadratic function, thus extending a theorem of Ernst Fi...

Convolution surfaces of quadratic triangular Bézier surfaces

In the present paper we prove that the polynomial quadratic triangular Bézier surfaces are LN-surfaces. We demonstrate how to reparameterize the surfaces such that the normals obtain linear coordinate functions. The close relation to quadratic Cremona transformations is elucidated. These reparameterizations can be effectively used for the computation of convolution surfaces.

Touch Screen Computer Displays

3d on Paper and Screen Displaying Three‐dimensional Figures Axonometric and Perspective Representation

The task of classical descriptive geometry is to produce precise, reconstructible drawings on three-dimensional figures; nowadays, in the case of drawings made by means of computer, this is often completed with movable, interactive parts. This work is a brief introduction to the axonometric and perspective representation, the tools for preparing descriptive images, keeping in view some principa...