## Kepler’s Laws of Planetary Motion

1. The orbit of every planet is an ellipse with the sun at one of the two foci, which can be calculated with:

$r=\frac{p}{1+\varepsilon\, \cos\theta},$

2. A line joining a planet and the sun sweeps out equal areas during equal intervals of time. i.e. The planet has to move faster when it is closer to the sun.

3. The Square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The exact relation, which is the same for both elliptical and circular orbits, is given by the equation

$P^2 = \frac{4 \pi^2}{ G(M_1 + M_2)} a^3,$

for masses M1 and M2, and Newton’s gravitational constant G.

Posted by on October 8, 2012 in Planet Generation, Research

## What is a Planet?

Planet: A Celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion, and has cleared its neighbourhood. i.e. Has become gravitationally dominant and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence. If it has met all other criteria except for clearing the neighbourhood, then it is classified as a dwarf planet – sorry Pluto and thank you Wikipedia.

If we go even further we can simplify them into two groups: gas giants and terrestrials, for the purpose of my research I will focus purely on the terrestrials.

Characteristics:

– Orbit: A planet revolves around the sun

– Axial Tilt: They lie at an angle to the plane of their stars’ equators, causing seasons.

– Rotation: They rotate around an invisible axes through their centre.

– Mass: the force of the planet’s own gravity forces the planet into a spherical shape.

– Internal Differentiation

– Atmosphere

– Magnetosphere

Posted by on October 8, 2012 in Planet Generation, Research

## Space Colonization for Trees

– Simplistic algorithm

– Able to specify a bounding volume for the growth of the trees

– Less trial and error needed to achieve realistic looking trees.

Posted by on October 4, 2012 in Planet Generation, Research

## Research Papers on Trees and Forest Generation

Posted by on October 3, 2012 in Planet Generation, Research

## Interesting Websites

Posted by on October 3, 2012 in Planet Generation, Research

## Articles 16/9

Rendering of Forests by applying volumetric “cells” onto the terrain.

http://www.antisphere.com/Research/Forest.php

Maths for Graphics

http://www.cs.brown.edu/~scd/facts.html

Trees

http://www.cs.duke.edu/courses/fall02/cps124/resources/p119-weber.pdf

Posted by on September 16, 2012 in Planet Generation, Research

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Gamasutra Article on Planet Generation

http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php

Isosurface Extraction Source

http://swiftcoder.wordpress.com/planets/isosurface-extraction/

A good reference for the terrain generation regarding marching cube techniques.