Approximate Differentiable Rendering with Algebraic Surfaces

Parametrization of approximate algebraic surfaces by lines

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ε-irreducible algebraic surfaces of degree d having an ε-singularity of multiplicity d − 1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance ε > 0 and an ε-irreducible algebraic surface V of degree d , t...

OpenDR: An Approximate Differentiable Renderer

Inverse graphics attempts to take sensor data and infer 3D geometry, illumination, materials, and motions such that a graphics renderer could realistically reproduce the observed scene. Renderers, however, are designed to solve the forward process of image synthesis. To go in the other direction, we propose an approximate differentiable renderer (DR) that explicitly models the relationship betw...

Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least-squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real-time rendering s...

ALGEBRAIC SURFACES WITH ' q

The simple method of distinguishing the underlying differentiable structures of algebraic surfaces

0 Introduction The purpose of this preprint is to construct a new invariant of the smooth structure of a simply connected 4-manifold M so called Spin-polynomials γ g,C and to show how to use it to compare the smooth structures of rational surfaces and surfaces of general type. This Spin-polynomial (0.1) is the analogue of the original Donaldson polynomial γ g (2, c 1 , c 2) ∈ S d H 2 (M, Z Z) (...