Beginning Math and Physics for Game Programmers
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Chapter 2, "Geometry Snippets"
Pythagorean Theorem
In a right triangle, the square of the length c of the hypotenuse is equal to the sum of the squares of the lengths a and b of the other two sides: c 2 = a 2 + b 2 . Distance Formula in 2D
where P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) are points on the line. Distance Formula in 3D
where P 1 ( x 1 , y 1 , z 1 ) and P 2 ( x 2 , y 2 , z 2 ) are points on the line. Midpoint Formula in 2D
is the midpoint between P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ). Midpoint Formula in 3D
is the midpoint between P 1 ( x 1 , y 1 , z 1 ) and P 2 ( x 2 , y 2 , z 2 ). Parabola with a Vertical Axis
y = a ( x “ h ) 2 + k , with vertex ( h , k ) and axis of symmetry x = h . Parabola with a Horizontal Axis
x = a ( y “ k ) 2 + h , with vertex ( h , k ) and axis of symmetry y = k . Equation of a Circle
( x “ h ) 2 + ( y “ k ) 2 = r 2 where the center is ( h , k ) and the radius is r . Equation of a Circle Centered at the Origin
x 2 + y 2 = r 2 where the center is (0,0) and the radius is r . Equation of a Sphere
( x “ h ) 2 + ( y “ k ) 2 + ( z “ l ) 2 = r 2 where the center is ( h , k , l ) and the radius is r . Equation of a Sphere Centered at the Origin
x 2 + y 2 + z 2 = r 2 where the center is (0,0,0) and the radius is r . Circle-Circle Collision Detection
Given two circles Optimized Circle-Circle Collision Detection
Given two circles Optimized Sphere-Sphere Collision Detection
Given two spheres |
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