There are changes occur to the terrain over time.

Geology Forces:

  • Volcano
  • Earthquakes
  • Plate tectomics
  • Erosion
    • Hydrolic: caused by water
    • Pneumatic: caused by air
    • Thermal: caused by heat
    • Chemical
      • Crystal
      • Salt
      • Lime + water

Hydrolic Erosion

Land Drains

The basic result of hydrolic erosion is that land drains.

Planchon-Darboux Algorithm:

In the new heightmap, find the lowest elevation, which is defined as:

  • each pixel.height >= original
  • each pixel.height > at least one neighbor .height
  • except the drains

Speed of Water

Generally speaking, the faster the water is, the more erosion there is.

The flat area does not erode, and the slopes erode fast, so the result is very steep cliffs.

  1. Planchon-Darboux
  2. Small amount of water everywhere (raining)
  3. Have water move down
  4. Erode as water moves (based on the slope and amount of water)

Better Model

How water affects the terrain?

  • Carries sediment
    • Amount of sediment kinetic energy

River sides

At turning of a river, the outside of the curve gradually gets larger, while the inside does not grow.

Land Slide

When water erode away dirt/rock near the river bed, rocks become hang by itself on the bank. When the erosion reach some threshold, the whole piece of land will slide down.

Wind Erosion

When there are plants, wind erosion does not affect the land.

When there are no plants, wind will blow away pieces over time, and forms round shapes on the rocks.

Wind blows slower close to surface. So if there is a large flat ground, wind erosion will be less severe. When there is sharp curves, there is not enough length to slow down, and thus causing faster erosion.

Thermal Erosion

Heat causes expansions, and coldness causes contraction. Rocks are rigid, not malleable, and thus the expansions/contractions will cause microfractures on the rocks, which will grow larger over time.

Salt Erosion


Crystallized Fracture Plains

Slow, high pressure deposition yields organized forms.

Lime + Water

When Height Map Fails


A voxel is a volume of pixels. 3-D array of pixels.

In each pixel, there are some fraction of rocks vs air.

Spheroidal Weathering: Pneumatic + Thermal - Smoothing effect

For each pixel, if neighbors have more rock than itself # low concavicity less weathering else more weathering based on the pixels with lower rock

if the function of concavicity and weathering is good, the weathering tends to create a sphere.

Marching Cubes Algorithm

The goal: Turn voxels into polygons

Connect the center of each cell -> a set of cubes

Determine whether each cell is inside rock or not, and based on that select a model of cube. Each model marks some boundary of the shape.

Lagrangian Simulation

A set of points along the border of air and rock. Calculate angle of neighboring points, and figure out how to move the pixel.


  1. Poor Spacing
  2. Topology changes, A non-hole shape -> a hole shape
  3. Delauney Triangulation

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