Circles

gistfile1.txt

function setup()
    FOV=45
    perspective(FOV)
    PM1=1/projectionMatrix()[1]
    ortho()
    pos=vec2(100,100) --circle position
    camPos=vec2(WIDTH/2,0) --fixed camera
    camDir=vec2(-0.5,1):normalize() --camera direction
    far=700
    fructum=mesh()
    local w=far*PM1*vec2(-camDir.y,camDir.x) 
    fructum.vertices={camPos,camPos+far*camDir-w,camPos+far*camDir+w}
    fructum:setColors(color(136, 168, 199, 255))
    --radius=50 --collision circle radius
    print("Fructum is in blue, pointing up")
    print("True tangent is in pink")
    print("Fake tangent is in green")
    print("Use your finger to drag the circle around")
    parameter.number("F",1,3,2.6)
    parameter.integer("radius",10,100,50)
end

function draw()
    background(150)
    fructum:draw()
    pushStyle()
    stroke(99, 124, 183, 255)
    strokeWidth(2)
    line(camPos.x,camPos.y,camPos.x+far*camDir.x,camPos.y+far*camDir.y)
    popStyle()
    DrawCircle()
end

function DrawCircle()
    local tangent=GetTangent(pos,radius,camPos,camDir)
    --calculate fake tangent
    local fake=pos+camDir*radius*F
    pushStyle()
    if IsVisible(pos,camPos,camDir,radius,far) then fill(255,255,0) else fill(255,255,0,100) end
    ellipse(pos.x,pos.y,radius*2)
    stroke(195, 72, 169, 255) strokeWidth(2)
    line(camPos.x,camPos.y,tangent.x,tangent.y)
    stroke(52, 162, 48, 255) 
    line(camPos.x,camPos.y,fake.x,fake.y)
    --ellipse(tangent.x,tangent.y,10)
    popStyle()
end

function GetTangent(centre,radius,camPos,camDir)
    --calculate offset from centre
    local s=(centre.x-camPos.x)/(-centre.y+camPos.y)
    local a=(radius/math.sqrt(1+s*s))*vec2(1,s)
    --now figure out which side of the circle is closest to the camera direction
    --this formula tells which side of a line, a point is on
    local d=camPos+camDir*1000
    local e=(centre.x-camPos.x)*(d.y-camPos.y)-(centre.y-camPos.y)*(d.x-camPos.x)
    if e>0 then return centre-a else return centre+a end --adjust the centre by the offset
end

function touched(t)
    pos=vec2(t.x,t.y)
end

--[[
function setup()
    FOV=45
    perspective(FOV)
    PM1=1/projectionMatrix()[1]
    ortho()
    pos=vec2(100,100) --circle position
    camPos=vec2(WIDTH/2,0) --fixed camera
    camDir=vec2(0,1)
    radius=5000000
    n=5000000
    t=os.time()
    for i=1,n do
        a=IsVisible(pos,camPos,camDir,radius)
    end
    print("True",os.time()-t)
    print(n/60/(os.time()-t))
end

function draw()
    
end
--]]

function IsVisible(pos,camPos,camDir,radius,far)
    local px,py,pcx,pcy,pdx,pdy,fx,fy=pos.x,pos.y,camPos.x,camPos.y,camDir.x,camDir.y
    --get tangent point
    local u=radius*2.6
    local tx,ty=px+pdx*u,py+pdy*u --tangent point
    --which side of LOS is our circle centre
    local dx,dy=pcx+pdx*1000,pcy+pdy*1000
    local IsOnLeft=(px-pcx)*(dy-pcy)-(py-pcy)*(dx-pcx)<0
    local wx,wy=-far*PM1*pdy,far*PM1*pdx 
    if IsOnLeft then 
        fx,fy=pcx+pdx*far+wx,pcy+pdy*far+wy --far left of frustum
        return (tx-pcx)*(fy-pcy)-(ty-pcy)*(fx-pcx)>0
    else
        fx,fy=pcx+pdx*far-wx,pcy+pdy*far-wy --far right of frustum
        return (tx-pcx)*(fy-pcy)-(ty-pcy)*(fx-pcx)<0
    end  
end

function GetTangent(centre,radius,camPos,camDir)
    local cx,cy,cpx,cpy,cdx,cdy=centre.x,centre.y,camPos.x,camPos.y,camDir.x,camDir.y
    --calculate offset from centre
    local s=(cx-cpx)/(-cy+cpy)
    local a=(radius/math.sqrt(1+s*s)) --*vec2(1,s)
    --now figure out which side of the circle is closest to the camera direction
    --this formula tells which side of a line, a point is on
    local dx,dy=cpx+cdx*1000,cpy+cdy*1000
    local e=(cx-cpx)*(dy-cpy)-(cy-cpy)*(dx-cpx)
    if e>0 then return vec2(cx-a,cy-s*a) else return vec2(cx+a,cy+s*a) end --adjust the centre by the offset
end

--[[
function IsVisible(pos,camPos,camLook,radius)
    local xDist=DistancePointToLine(pos,camPos,camLook)
    return xDist-radius<camPos:dist(pos)/projectionMatrix()[1]*1.1
end

function DistancePointToLine(p,a,b)
    b=p+(b-a)*5000
    return (p-a):dist(math.max(math.min((p-a):dot(b-a)/(b-a):lenSqr(),1),0)*(b-a))
end
--]]