Modeling and Rendering of Weathered Stone

SIGGRAPH 1999

Julie Dorsey Alan Edelman Henrik Wann Jensen Justin Legakis Hans Kohling Pedersen

M.I.T.

Andrea RowanFebruary 16, 2001

Outline

Problem description Previous Work System

– Slab data structure– Stone weathering model– Light scattering

Results Successes / Problems

Problem Description

Visually represent the weathering of stone

Chemical weathering - erosion by water, pollutants

Processes to Model

Movement of water– Porous stone

Dissolution/recrystallization of minerals– Oxides of Carbon, Sulfur, Nitrogen

Chemical transformation of minerals– Affects stone’s appearance

Deposition of atmospheric pollution– Airborne pollution or acid rain

How is This Model Unique?

Volume Monitoring– Slab data structure

Simulation– Water flow– Transport/Dissolution of minerals– Surface erosion

Subsurface scattering of light

Previous Work

Volume modeling– Voxels (Kaufman et al. [16])

High storage + calculation requirements

– Shells (Udupa et al. [34]) Set of voxels near surface boundary Axis-aligned

Subsurface Light Scattering– Dorsey et al. [7], Hanrahan et al. [12]

Assume homogeneous layers of surface

Previous Work

Weathering effects– 2D effects

Water flow (Dorsey et al. [7],[8]) Watercolors (Curtis et al. [6])

– Erosion of fractal terrains (Musgrave et al. [20])

Drop water on surface, let it run down surface collecting and depositing minerals

Doesn’t account for different minerals/rocks

System Architecture

Input– Polyhedral mesh– Water maps– Mineral deposit maps

Voxelizer Quarry Weathering Simulator Polygonizer Renderer

Voxels

Store mineral properties 3-D stone density function s No stone present

– s = 0 Decay index d

– Tendancy to erode to clay

Slabs

Groups of Voxels Surface-Aligned 8-cornered Separated by bilinear patches Slab edges are average of area normals

Quarry

Rendering of Unweathered Stone Combination of solid 3D procedural

textures Noise function

– Mineral patterns of granite– Veins of marble

Weathering Simulation

2-D stone surface– Stone meets outside environment– Water evaporates from stone

3-D Weathered interior– Grows during wet cycles

Interior moist/dry front– Internal boundary

Travel of Moisture

Darcy’s law shows fluid speed in stone:

v = -K/(p - g)

v = velocity of front of fluid (calculated)K = permeability of stone (input constant) = viscosity, or resistance to flow (input constant)p = pressure of water on surface (varying) = density of water (input constant)g = gravity (input constant)

Travel of Moisture

Location of front at any time t:

dp/dt = -·(p) = -2p - ·p

= porosity, or the ratio: volume of empty space/volume of

mass in stone (input constant)

p = pressure of water on surface (varying)

Travel of Moisture

Location of moisture evolved through time with loop:– Solve dp/dt with current pressure p

Internal front External surface pressure (varies as go from

wet to dry seasons)

– Update front location with Darcy’s law (showing v of front)

Dissolution/Recrystallization

Dissolution calculated at internal front:

dCi/dt = - ki(mi - Ci)

Ci = Concentration of dissolved mineral in the water (Calculated)

ki = Solubility of the mineral m (input constant)

mi = Saturated level (puts limit on dissolution) (Calculated)i = Mineral index

Mineral movement

Convective-diffusion equation:

/t(Ci) + v·(Ci) = ·(DiCi)

= porosity (input constant)

Ci = Concentration of dissolved mineral in the water (calculated)

v = velocity from pressure gradient (calculated)

Di = Diffusivity of mineral (input constant)

Mineral movement

Minerals form crust on surface Green’s theorem preserves total mass Decay index (d) of each voxel is

continuously modified as minerals are dissolved/deposited.

Numerical Calculations

Finite Difference Schemes– Solves gradient problem

Slabs can be trapezoidal– Laplacian (2) calculation is complicated

Light Scattering

Stone contains transparent crystal grains

Must consider subsurface scattering of light

Light Scattering

Mie scattering (back & forward!)– Light hits a particle or a molecule whose

diameter is >= the wavelength of the light

Light Scattering

Scattered Radiance

Ls = Ld+ Li

– Ld = Radiance from direct illumination Shadow ray from light source

– Li = Radiance from indirect illumination Photon map estimate (Photons emitted from light

sources)

Results

Simulations:– Quad 250 MHz R10000 SGI

Renderings:– Dual 400 MHz Pentium II PC with Linux

Sphinx

2.2 million triangles 281 slabs, 323 voxels each Simulation - 24 hours Rendering - 80 minutes

Sphinx

Sandstone Column

100,000 triangles 240 slabs, 323 voxels each Simulation - 4 hours Rendering - 30 minutes

Sandstone Column

Successes

Scientifically-based model with few hacks!

Realistic looking results Good framework for diversity of effects

– Easy to implement salt-water erosion

Problems

Slabs are edited by hand to fix overlapping

Slow computation time– Can’t interactively weather the stone!

Limited by lack of complete scientific knowledge

References

Dorsey et al. Modeling and Rendering of Weathered Stone. SIGGRAPH Conference Proceedings, 1999.

Musgrave et al. The Synthesis and Rendering of Eroded Fractal Terrains. Computer Graphics, July 1989.

Udupa et al. Shell Rendering. IEEE Computer Graphics and Applications, November 1993.