Maths & trigonometry cheat sheet for 2D games

readme.md

Conventions

• o = [xo = 0, yo = 0] is the origin
• A = [xA, yA] is a point on the 2D plane. Same for B, C, ...
• lengths are in any unit (ex: pixels)
• code snippets are in JavaScript

Degrees to radians

angleRad = angleDeg * Math.PI / 180;

Radians to degrees

angleDeg = angleRad * 180 / Math.PI;

Distance between two points (Pythagore)

• dist = function(A,B){ return Math.sqrt((xB - xA)*(xB - xA) + (yB - yA)*(yB - yA)) } // ES5
• dist = (A, B) => Math.hypot(xB -xA, yB -yA) // ES6

Line passing through 2 points

• line equation: y = ax + b
• a = (yB - yA) / (yB - yA) = tan θ
• θ = angle between line and x axis
• b = yA - a * xA (because yA = a * xA + b)

Angle in radians between the x axis at the origin and a point on the plane

angle = Math.atan2(Ax, Ay)

Angle in radians between two points

angle = Math.atan2(By - Ay, Bx - Ax);

Rotate a point (angle in radians)

• Anew_x = Ax * Math.cos(angle) - Ay * Math.sin(angle)
• Anew_y = Ax * Math.sin(angle) + Ay * Math.cos(angle)

Project a point on the trigonometric circle

• Anew_x = Math.cos(atan2(Ax, Ay))
• Anew_y = Math.sin(atan2(Ax, Ay))

Intersections between a line and the grid (2D raycasting)

• http://www.cse.yorku.ca/~amana/research/grid.pdf
• http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm