Frustum test2

gistfile1.txt

function setup()
    FOV=45
    perspective(FOV)
    PM1=1/projectionMatrix()[1]
    ortho()
    pos=vec2(100,100) --circle position
    camPos=vec2(WIDTH/2,HEIGHT/2) --fixed camera
    --camDir=vec2(0.25,1):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")
    print("The circle goes bright yellow when it enters the frustum")
    parameter.integer("radius",10,100,50)
    parameter.integer("angle",0,360,0,SetAngle)
end

function SetAngle()
    camDir=vec2(math.cos(math.rad(angle)),math.sin(math.rad(angle)))
    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))
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

local dx,dy,f1x,f1y,f2x,f2y,PM1,cosFOV
local sqrt=math.sqrt

function DrawCircle()
    --local tangent=GetTangent(pos,radius,camPos,camDir)
    --calculate fake tangent
    local fake=pos+camDir*radius*2.6
    pushStyle()
    cosFOV=math.cos(math.rad(FOV/2))
    cosFOV2=cosFOV*cosFOV
    if IsVisible3(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
    pos=vec2(100,100) --circle position
    camPos=vec2(WIDTH/2,0) --fixed camera
    camDir=vec2(0,1)
    radius=50
    n=20000000
    cosFOV=math.cos(math.rad(FOV/2))
    cosFOV2=cosFOV*cosFOV
    t=os.time()
    for i=1,n do
        a=IsVisible(pos,camPos,camDir,radius)
    end
    print("Non vector",os.time()-t)
    print(n/60/(os.time()-t))
    t=os.time()
    for i=1,n do
        a=IsVisible3(pos,camPos,camDir,radius)
    end
    print("Vector",os.time()-t)
    print(n/60/(os.time()-t))
end

function draw()
    
end
--]]

function IsVisible(pos,camPos,camDir,radius)
    local px,py,pcx,pcy,pdx,pdy=pos.x,pos.y,camPos.x,camPos.y,camDir.x,camDir.y
    local u=radius*2.6
    local ptx,pty=px+pdx*u-pcx,py+pdy*u-pcy
    local sq=sqrt(ptx*ptx+pty*pty)
    return (ptx*pdx+pty*pdy)>cosFOV*sq
end

function IsVisible2(pos,camPos,camDir,radius)
    local v=(pos+camDir*(radius*2.6)-camPos):normalize()
    return v:dot(camDir)>cosFOV
end

function IsVisible3(pos,camPos,camDir,radius)
    local px,py,pcx,pcy,pdx,pdy=pos.x,pos.y,camPos.x,camPos.y,camDir.x,camDir.y
    local u=radius*2.6
    local ptx,pty=px+pdx*u-pcx,py+pdy*u-pcy
    local sq=ptx*ptx+pty*pty
    local a=ptx*pdx+pty*pdy
    return a*a>cosFOV2*sq
end