Class: Ra::Shape::Sphere

Inherits:
Base
  • Object
show all
Defined in:
lib/ra/shape/sphere.rb

Overview

A sphere at origin <0,0,0> with a radius 1. A sphere surface is defined:

x² + y² + z² = radius²

A unit radius simplifies further:

x² + y² + z² = 1

A ray x / y / z values at t use the origin and direction:

x = origin.x + direction.x * t
y = origin.y + direction.y * t
z = origin.z + direction.z * t

Substituting x / y / z allows for solving for t:

1 = (origin.x + direction.x * t)²
  + (origin.y + direction.y * t)²
  + (origin.z + direction.z * t)²

Simplifying gives us a quadratic formula with terms defined as:

a = direction.x² + direction.y² + direction.z²
b = 2 * ((origin.x * direction.x) + (origin.y * direction.y) + (origin.z * direction.z))
c = origin.x² + origin.y² + origin.z² - 1
discriminant = b² - 4ac
t = (-b ± √discriminant) / (2a)

A discriminant <0 indicates the ray does not intersect the sphere.

Instance Attribute Summary

Attributes inherited from Base

#material, #transform

Method Summary

Methods inherited from Base

#color, #initialize, #intersect, #normal

Constructor Details

This class inherits a constructor from Ra::Shape::Base