[vec] Add parallax factor to toworldcoords() and toscreencoords()

algo.lua

@@ -5,25 +5,10 @@
 -- @author Lorenzo Cogotti
 
 local floor = math.floor
-local min, max = math.min, math.max
 
 local algo = {}
 
 
---- Clamp x within range [a,b] (where b >= a).
---
--- @number x value to clamp.
--- @number a interval lower bound (inclusive).
--- @number b interval upper bound (inclusive).
--- @treturn number clamped value.
-function algo.clamp(x, a, b) return min(max(x, a), b) end
-
---- Sign function.
---
--- @number x value whose sign should be returned.
--- @treturn number sign of x, -1 if negative, 1 if positive, 0 otherwise.
-function algo.sign(x) return x > 0 and 1 or x < 0 and -1 or 0 end
-
 --- Fast remove from array.
 --
 -- Replace 'array[i]' with last array's element and

color.lua

@@ -38,6 +38,50 @@ function Color.lighten(r, g, b, amount)
 	return r, g, b
 end
 
+function Color.hsl(h, s, l, a)
+	a = a or 1
+	if s <= 0 then return 1, 1, 1, a end
+
+	h = h * 6
+
+	local abs = math.abs
+	local c = (1 - abs(l*2 - 1))*s
+	local x = (1 - abs(h%2 - 1))*c
+	local m = l - c*0.5
+
+	local r, g, b
+	if h < 1 then     r, g, b = c, x, 0
+	elseif h < 2 then r, g, b = x, c, 0
+	elseif h < 3 then r, g, b = 0, c, x
+	elseif h < 4 then r, g, b = 0, x, c
+	elseif h < 5 then r, g, b = x, 0, c
+	else              r, g, b = c, 0, x
+	end
+	return r+m, g+m, b+m, a
+end
+
+function Color.hsv(h, s, v, a)
+	a = a or 1
+	if s <= 0 then return v, v, v, a end
+
+	h = h * 6
+
+	local c = v * s
+	local x = (1 - math.abs(h%2 - 1))*c
+	local m = v - c
+
+	local r, g, b
+	if h < 1 then     r, g, b = c, x, 0
+	elseif h < 2 then r, g, b = x, c, 0
+	elseif h < 3 then r, g, b = 0, c, x
+	elseif h < 4 then r, g, b = 0, x, c
+	elseif h < 5 then r, g, b = x, 0, c
+	else              r, g, b = c, 0, x
+	end
+	return r+m, g+m, b+m, a
+
+end
+
 --- Given two RGB colors, calculate fade by the specified amount.
 --
 -- @number cr first color, red channel

init.lua

@@ -14,6 +14,7 @@ local BASE = (...)..'.'
 
 return {
     algo = require(BASE..'algo'),
+    mathx = require(BASE..'mathx'),
     meta = require(BASE..'meta'),
     rect = require(BASE..'rect'),
     shadowtext = require(BASE..'shadowtext'),

mathx.lua

@@ -0,0 +1,142 @@
+--- Extended math functions
+--
+-- @module gear.mathx
+-- @copyright 2022 The 1414 Code Forge
+-- @author Lorenzo Cogotti
+
+local floor = math.floor
+local min, max = math.min, math.max
+local cos, pi = math.cos, math.pi
+local random = love and love.math.random or math.random
+
+local mathx = setmetatable({}, math)
+
+
+--- Clamp x within range [a,b] (where b >= a).
+--
+-- @number x value to clamp.
+-- @number a interval lower bound (inclusive).
+-- @number b interval upper bound (inclusive).
+-- @treturn number clamped value.
+function mathx.clamp(x, a, b) return min(max(x, a), b) end
+
+--- Sign function.
+--
+-- @number x value whose sign should be returned.
+-- @treturn number sign of x, -1 if negative, 1 if positive, 0 otherwise.
+function mathx.sign(x) return x > 0 and 1 or x < 0 and -1 or 0 end
+
+--- sign() variant returning 1 if x is non-negative.
+--
+-- @number x value whose sign should be returned.
+-- @treturn number sign of x, -1 if negative, 1 if non-negative.
+function mathx.sign2(x) return x >= 0 and 1 or -1 end
+
+--- Linear interpolation between a and b.
+--
+-- @number a first interpolation point.
+-- @number b second interpolation point.
+-- @number t the interpolation factor, a real number within [0,1].
+-- @treturn number the interpolated value.
+function mathx.lerp(a, b, t) return a*(1 - t) + b*t end
+
+--- Less accurate, but slightly faster, variant of lerp().
+function mathx.lerp2(a, b, t) return a + (b - a)*t end
+
+--- Cosine interpolation between a and b.
+--
+-- @number a first interpolation point.
+-- @number b second interpolation point.
+-- @number t the interpolation factor, a real number within [0,1].
+-- @treturn number interpolated value.
+function mathx.cerp(a, b, t)
+	local tt = (1 - cos(t * pi)) * 0.5
+	return a*(1 - tt) + b*tt
+end
+
+--- Cubic interpolation between a, b, c and d.
+--
+-- @number a first interpolation point.
+-- @number b second interpolation point.
+-- @number c third interpolation point.
+-- @number d fourth interpolation point.
+-- @number t the interpolation factor, a real number within [0,1].
+-- @treturn number the interpolated value.
+function mathx.cberp(a, b, c, d, t)
+	local tt = t * t
+	local a0 = d - c - a + b
+	return a0*t*tt + (a - b - a0)*tt + (c - a)*t + b
+end
+
+--- Catmull-Rom spline interpolation between a, b, c and d.
+--
+-- @number a first interpolation point.
+-- @number b second interpolation point.
+-- @number c third interpolation point.
+-- @number d fourth interpolation point.
+-- @number t the interpolation factor, a real number within [0,1].
+-- @treturn number the interpolated value.
+function mathx.catmullrom(a, b, c, d, t)
+	local tt  =  t * t
+	local mha = -a * 0.5
+	local hd  =  d * 0.5
+	return (mha + 1.5*b - 1.5*c + hd)*t*tt + (a - 2.5*b + 2*c - hd)*tt + (mha + 0.5*c)*t + b
+end
+
+--- Hermite interpolation between a, b, c and d.
+--
+-- @number a first interpolation point.
+-- @number b second interpolation point.
+-- @number c third interpolation point.
+-- @number d fourth interpolation point.
+-- @number t the interpolation factor, a real number within [0,1].
+-- @number tension the tension factor, 1 is high, 0 normal (default), -1 is low.
+-- @number bias the bias factor, 0 is even (default), positive is towards the first segment, negative towards the other.
+-- @treturn number the interpolated value.
+function mathx.herp(a, b, c, d, t, tension, bias)
+	tension = tension or 0
+	bias = bias or 0
+
+	local b0 = 1 + bias
+	local b1 = 1 - bias
+	local ht = (1 - tension) * 0.5
+	local s0 = b0 * ht
+	local s1 = b1 * ht
+
+	local tt   = t   * t
+	local ttt  = tt  * t
+	local ttt2 = ttt * 2
+	local tt3  = tt  * 3
+
+	local m0 = (b - a)*s0 + (c - b)*s1
+	local m1 = (c - b)*s0 + (d - c)*s1
+
+	local a0 = ttt2 - tt3  + 1
+	local a1 = ttt  - tt*2 + t
+	local a2 = ttt  - tt
+	local a3 = tt3  - ttt2
+
+	return a0*b + a1*m0 + a2*m1 + a3*c
+end
+
+--- Pseudo-random sign value.
+--
+-- @treturn number the pseudo-random sign value, either -1, 0, or 1.
+function mathx.rsign() return random(-1, 1) end
+
+--- rsign() variant returning -1 or 1.
+--
+-- @treturn number the pseudo-random sign value, either -1 or 1.
+function mathx.rsign2() return random(2) == 2 and 1 or -1 end
+
+--- Precise pseudo-random number within [min,max] (where max >= min).
+--
+-- @number min interval lower bound (inclusive).
+-- @number max interval upper bound (inclusive).
+-- @treturn number the pseudo-random real number within [a,b].
+function mathx.prandom(min, max)
+	local t = random()
+	return min * (1 - t) + max * t
+end
+
+return mathx

timer.lua

@@ -74,7 +74,7 @@ function Timer:after(delay, func)
 end
 
 function Timer:every(delay, after, count)
-    local count = count or math.huge -- exploit below: math.huge - 1 = math.huge
+    count = count or math.huge -- exploit below: math.huge - 1 = math.huge
     local handle = {
         time = 0,
         during = _nothing_,

vec.lua

@@ -206,66 +206,72 @@ function vec.angleto(x1,y1, x2,y2) return atan2(y1,x1) - atan2(y2,x2) end
 
 --- Transform world coordinates to screen coordinates.
 --
--- @param x (number) World coordinate X.
--- @param y (number) World coordinate Y.
--- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
--- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
--- @param rot (number|nil) View rotation in radians, defaults to 0.
--- @param scale (number|nil) View scale (zoom), defaults to 1.
--- @param left (number|nil) Viewport left corner, defaults to 0.
--- @param top (number|nil) Viewport top corner, defaults to 0.
--- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
--- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
+-- @number x World coordinate X.
+-- @number y World coordinate Y.
+-- @number xview Point of view X coordinate, defaults to w/2.
+-- @number yview Point of view Y coordinate, defaults to h/2.
+-- @number rot View rotation in radians, defaults to 0.
+-- @number scale View scale (zoom), defaults to 1.
+-- @number left Viewport left corner, defaults to 0.
+-- @number top Viewport top corner, defaults to 0.
+-- @number w Viewport width, defaults to love.graphics.getWidth().
+-- @number h Viewport height, defaults to love.graphics.getHeight().
+-- @number xparallax Parallax factor over X, defaults to 1.
+-- @number yparallax Parallax factor over Y, defaults to 1.
 --
 -- @return (x,y) Transformed to screen coordinates according to
 --         viewport and offset.
-function vec.toscreencoords(x,y, vx,vy, rot, scale, left,top, w,h)
+function vec.toscreencoords(x,y, xview,yview, rot, scale, left,top,w,h, xparallax,yparallax)
     left,top = left or 0, top or 0
     w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
 
     local halfw,halfh = w/2, h/2
 
-    vx,vy = vx or halfw, vy or halfh
+    xview,yview = xview or halfw, yview or halfh
     rot = rot or 0
     scale = scale or 1
+    xparallax,yparallax = xparallax or 1, yparallax or 1
 
     local sina,cosa = sin(rot),cos(rot)
 
-    x,y = x - vx, y - vy
+    x,y = x - xview*xparallax, y - yview*yparallax
     x,y = cosa*x - sina*y, sina*x + cosa*y
     return x*scale + halfw + left, y*scale + halfh + top
 end
 
 --- Transform screen coordinates to world coordinates.
 --
--- @param x (number) Screen coordinate X.
--- @param y (number) Screen coordinate Y.
--- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
--- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
--- @param rot (number|nil) View rotation in radians, defaults to 0.
--- @param scale (number|nil) View scale (zoom), defaults to 1.
--- @param left (number|nil) Viewport left corner, defaults to 0.
--- @param top (number|nil) Viewport top corner, defaults to 0.
--- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
--- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
+-- @number x Screen coordinate X.
+-- @number y Screen coordinate Y.
+-- @number xview Point of view X coordinate, defaults to w/2.
+-- @number yview Point of view Y coordinate, defaults to h/2.
+-- @number rot View rotation in radians, defaults to 0.
+-- @number scale View scale (zoom), defaults to 1.
+-- @number left Viewport left corner, defaults to 0.
+-- @number top Viewport top corner, defaults to 0.
+-- @number w Viewport width, defaults to love.graphics.getWidth().
+-- @number h Viewport height, defaults to love.graphics.getHeight().
+-- @number xparallax Parallax factor over X, defaults to 1.
+-- @number yparallax Parallax factor over Y, defaults to 1.
 --
 -- @return (x,y) Transformed to world coordinates according to
 --         viewport and offset.
-function vec.toworldcoords(x,y, vx,vy, rot, scale, left,top,w,h)
+function vec.toworldcoords(x,y, xview,yview, rot, scale, left,top,w,h, xparallax,yparallax)
     left, top = left or 0, top or 0
     w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
 
     local halfw,halfh = w/2, h/2
 
-    vx,vy = vx or halfw, vy or halfh
+    xview,yview = xview or halfw, yview or halfh
     rot = rot or 0
     scale = scale or 1
+    xparallax,yparallax = xparallax or 1, yparallax or 1
 
     local sina,cosa = sin(-rot),cos(-rot)
 
     x,y = (x - halfw - left) / scale, (y - halfh - top) / scale
     x,y = cosa*x - sina*y, sina*x + cosa*y
-    return x+vx, y+vy
+    return x + xview*xparallax, y + yview*yparallax
 end
 
 return vec