136 lines
3.4 KiB
Lua
136 lines
3.4 KiB
Lua
--- Axis-aligned rectangles.
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--
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-- Function for basic bounding rectangles building and testing.
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--
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-- @module gear.rect
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-- @copyright 2022 The DoubleFourteen Code Forge
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-- @author Lorenzo Cogotti
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local rotatesincos = require((...):gsub('rect$', '')..'vec').rotatesincos
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local min, max = math.min, math.max
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local abs = math.abs
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local rect = {}
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--- Extend rectangle to include a point.
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function rect.expand(x,y,w,h, px,py)
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if w < 0 or h < 0 then
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return px,py,0,0
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end
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local xw, yh
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x = min(x, px)
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y = min(y, py)
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xw = max(x+w, px)
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yh = max(y+h, py)
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return x, y, xw-x, yh-y
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end
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--- Calculate and return the union of two rectangles.
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function rect.union(x1,y1,w1,h1, x2,y2,w2,h2)
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local xw1,yh1, xw2,yh2
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if w1 < 0 or h1 < 0 then
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local huge = math.huge
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x1,y1,xw1,yh1 = huge,huge,-huge,-huge
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else
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xw1,yh1 = x1 + w1,y1 + h1
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end
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if w2 < 0 or h2 < 0 then
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local huge = math.huge
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x2,y2,xw2,yh2 = huge,huge,-huge,-huge
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else
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xw2,yh2 = x2 + w2,y2 + h2
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end
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x1 = min(x1, x2)
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y1 = min(y1, y2)
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xw1 = max(xw1, xw2)
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yh1 = max(yh1, yh2)
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return x1, y1, xw1 - x1, yh1 - y1
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end
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--- Calculate and return the intersection between two rectangles.
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function rect.intersection(x1,y1,w1,h1, x2,y2,w2,h2)
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if w1 < 0 or h1 < 0 then
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return x1,y1,w1,h1
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elseif w2 < 0 or h2 < 0 then
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return x2,y2,w2,h2
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end
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local xw1,yh1 = x1+w1, y1+h1
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local xw2,yh2 = x2+w2, y2+h2
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x1 = max(x1, x2)
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y1 = max(y1, y2)
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xw1 = min(xw1, xw2)
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yh1 = min(yh1, yh2)
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return x1,y1, xw1-x1,yh1-y1
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end
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--- Rotate rectangle around (ox,oy) about rot radians,
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-- and return the result's minimum enclosing
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-- axis-aligned rectangle.
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--
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-- NOTE: This causes precision loss, possibly generating
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-- larger bounds than needed for the rotated geometry
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-- Don't use this function repeatedly on the same bounds.
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function rect.rotate(rx,ry,rw,rh, rot, ox,oy)
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if rw < 0 or rh < 0 then
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return rx,ry,rw,rh
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end
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ox = ox or 0
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oy = oy or 0
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local sina,cosa = sin(rot),cos(rot)
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local x1,y1 = rotatesincos(rx, ry, sina,cosa, ox,oy)
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local x2,y2 = rotatesincos(rx+rw, ry, sina,cosa, ox,oy)
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local x3,y3 = rotatesincos(rx+rw, ry+rh, sina,cosa, ox,oy)
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local x4,y4 = rotatesincos(rx, ry+rh, sina,cosa, ox,oy)
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local rxw, rxh
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rx = min(min(min(x1, x2), x3), x4)
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ry = min(min(min(y1, y2), y3), y4)
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rxw = max(max(max(x1, x2), x3), x4)
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ryh = max(max(max(y1, y2), y3), y4)
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return rx,ry, rxw-rx,ryh-ry
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end
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--- Test whether point (x,y) lies inside a rectangle.
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function rect.pointinside(x,y, rx,ry,rw,rh)
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return x >= rx and y >= ry and x-rx <= rw and y-ry <= rh
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end
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--- Test whether the first rectangle lies inside the second.
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function rect.rectinside(x1,y1,w1,h1, x2,y2,w2,h2)
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return (x1 >= x2 and y1 >= y2 and w1 <= w2 and h1 <= h2 and w2 >= 0 and h2 >= 0)
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or ((w1 < 0 or h1 < 0) and (w2 >= 0 and h2 >= 0))
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end
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--- Test two rectangles for equality with optional epsilon.
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function rect.eq(x1,y1,w1,h1, x2,y2,w2,h2, eps)
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eps = eps or 0.007
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return (abs(x1 - x2) <= eps and
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abs(y1 - y2) <= eps and
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abs(w1 - w2) <= eps and
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abs(h1 - h2) <= eps)
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or ((w1 < 0 or h1 < 0) and (w2 < 0 or h2 < 0))
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end
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--- Test whether a rectangle is empty.
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function rect.isempty(x,y,w,h)
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return w < 0 or h < 0
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end
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return rect
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