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| − | This page lists mathematical functions which are useful in game programming. They are generally short, simple, and optimal.
| + | #REDIRECT [[General math]] |
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| − | <source lang="lua">
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| − | -- Averages an arbitrary number of angles (in radians).
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| − | function math.averageAngles(...)
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| − | local x,y = 0,0
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| − | for i=1,select('#',...) do local a= select(i,...) x, y = x+math.cos(a), y+math.sin(a) end
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| − | return math.atan2(y, x)
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| − | end
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| − | -- Returns the distance between two points.
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| − | function math.dist(x1,y1, x2,y2) return ((x2-x1)^2+(y2-y1)^2)^0.5 end
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| − | -- Returns the angle between two points.
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| − | function math.angle(x1,y1, x2,y2) return math.atan2(x2-x1, y2-y1) end
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| − | -- Returns the closest multiple of 'size' (defaulting to 10).
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| − | function math.multiple(n, size) size = size or 10 return math.round(n/size)*size end
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| − | -- Clamps a number to within a certain range.
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| − | function math.clamp(low, n, high) return math.min(math.max(low, n), high) end
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| − | -- Linear interpolation between two numbers.
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| − | function lerp(a,b,t) return a+(b-a)*t end
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| − | -- Cosine interpolation between two numbers.
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| − | function cerp(a,b,t) local f=(1-math.cos(t*math.pi))*.5 return a*(1-f)+b*f end
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| − | -- Normalize two numbers.
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| − | function math.normalize(x,y) local l=(x*x+y*y)^.5 if l==0 then return 0,0,0 else return x/l,y/l,l end end
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| − | -- Returns 'n' rounded to the nearest 'deci'th (defaulting whole numbers).
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| − | function math.round(n, deci) deci = 10^(deci or 0) return math.floor(n*deci+.5)/deci end
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| − | -- Randomly returns either -1 or 1.
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| − | function math.rsign() return math.random(2) == 2 and 1 or -1 end
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| − | -- Returns 1 if number is positive, -1 if it's negative, or 0 if it's 0.
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| − | function math.sign(n) return n>0 and 1 or n<0 and -1 or 0 end
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| − | -- Checks if two lines intersect (or line segments if seg is true)
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| − | -- Lines are given as four numbers (two coordinates)
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| − | function findIntersect(l1p1x,l1p1y, l1p2x,l1p2y, l2p1x,l2p1y, l2p2x,l2p2y, seg1, seg2)
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| − | local a1,b1,a2,b2 = l1p2y-l1p1y, l1p1x-l1p2x, l2p2y-l2p1y, l2p1x-l2p2x
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| − | local c1,c2 = a1*l1p1x+b1*l1p1y, a2*l2p1x+b2*l2p1y
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| − | local det,x,y = a1*b2 - a2*b1
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| − | if det==0 then return false, "The lines are parallel." end
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| − | x,y = (b2*c1-b1*c2)/det, (a1*c2-a2*c1)/det
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| − | if seg1 or seg2 then
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| − | local min,max = math.min, math.max
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| − | if seg1 and not (min(l1p1x,l1p2x) <= x and x <= max(l1p1x,l1p2x) and min(l1p1y,l1p2y) <= y and y <= max(l1p1y,l1p2y)) or
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| − | seg2 and not (min(l2p1x,l2p2x) <= x and x <= max(l2p1x,l2p2x) and min(l2p1y,l2p2y) <= y and y <= max(l2p1y,l2p2y)) then
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| − | return false, "The lines don't intersect."
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| − | end
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| − | end
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| − | return x,y
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| − | end
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| − | </source>
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| − | | |
| − | == Contributors ==
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| − | * [[User:Taehl|Taehl]]
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| − | | |
| − | [[Category:Snippets]]
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| − | {{#set:Author=User:Taehl}}
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| − | {{#set:Description=A collection of mathematical functions which are useful in game programming.}}
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| − | == Other Languages ==
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| − | {{i18n|Additional math}}
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