Polynomial methods for Procedural Terrain Generation

TL;DR

This paper introduces a novel polynomial-based method for procedural 3D terrain and texture generation that outperforms traditional fractal noise techniques in speed while maintaining high quality, with comprehensive analysis and comparison.

Contribution

The paper presents a new polynomial approach for terrain generation that is faster and more flexible than existing gradient noise methods, applicable to multiple dimensions.

Findings

Faster terrain generation compared to Perlin and OpenSimplex noise.

Results of comparable visual quality to traditional methods.

Fractal analysis shows realistic terrain characteristics.

Abstract

A new method is presented, allowing for the generation of 3D terrain and texture from coherent noise. The method is significantly faster than prevailing fractal brownian motion approaches, while producing results of equivalent quality. The algorithm is derived through a systematic approach that generalizes to an arbitrary number of spatial dimensions and gradient smoothness. The results are compared, in terms of performance and quality, to fundamental and efficient gradient noise methods widely used in the domain of fast terrain generation: Perlin noise and OpenSimplex noise. Finally, to objectively quantify the degree of realism of the results, a fractal analysis of the generated landscapes is performed and compared to real terrain data.