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Copy pathhyperbolicPlay1.7_intersectionDemo.bb
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hyperbolicPlay1.7_intersectionDemo.bb
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Graphics 700,700
R = 300
Type point
Field id
Field x#,y#
Field u#,v#
Field tu#, tv#
Field r,g,b
Field links.point[100]
Field numlinks
Field mouseControlled
Field show
Field toDelete
End Type
Type interPoint
Field x#, y#
Field p1x#, p1y#
Field p2x#, p2y#
End Type
Type camera
Field id
Field x#, y#
Field orient#
Field snap.point
Field yparity
;virtual camera that ignores boundaries
Field vx#, vy#
Field vorient#
End Type
Type boundary
Field x1#,y1#
Field x2#,y2#
End Type
n = 3
k = 7
;init(n,k)
cam.camera = New camera
cam\x = 0.5
cam\y = 1.5
cam\orient = 30
p1.point = createPoint(0,0, 255,0,0, 1)
p2.point = createPoint(1,0, 255,0,255, 1)
p1\numLinks = 1
p1\links[1] = p2
p3.point = createPoint(0.5,1, 0,0,255, 1)
p4.point = createPoint(1.5,-1, 0,255,255, 1)
p3\numLinks = 1
p3\links[1] = p4
Local out#[2]
intersection(p1\x,p1\y, p2\x,p2\y, p3\x,p3\y, p4\x,p4\y, out)
p5.point = createPoint(out[1],out[2], 255,255,0, 1)
cam\snap = First point
draw(R)
SetBuffer(BackBuffer())
While Not KeyHit(1)
If getInput(R)
Cls
draw(R)
Flip
EndIf
Wend
End
Function init(n,k)
; n = 3 ;polygons around a point
theta# = 360./n
; k = 7 ;sides per polygon
phi# = 360./k
numer# = (1+Cos(phi))*Cos(theta/2)
denom# = Sin(phi)*Sin(theta/2)
dis# = Sqr( (numer/denom)^2 - 1 )
; rad# = cosh(dis)
; rad2# = acosh(dis)
; DebugLog "dis = "+dis+", rad = "+rad+", rad2 = "+rad2+", cosh(rad2) = "+cosh(rad2)
; DebugLog invTransform(0.95,0,1)+","+invTransform(0.95,0,2)
; rad# = (1+(dis^2)*(1-Cos(phi)))
; rad# = 2*dis^2*(1-Cos(phi)) + dis^4*(1-Cos(phi))^2
rad# = dis*(Sqr(1+dis^2)*(1-Cos(phi))*Cos(theta/2) + Sin(phi)*Sin(theta/2))
distanceLimit = 50^2
limit = 1000
tolerance# = 0.1
Local queue.point[10000]
Local ao#[10000] ;angle offset
center.point = Null
p2.point = Null
np.point = Null
q = 2
queue[1] = createPoint(0,0)
queue[2] = createPoint(0,-rad)
queue[2]\numLinks = 1
queue[2]\links[1] = queue[1]
ao[1] = -90
ao[2] = 90
cam.camera = New camera
cam\id = 1
cam\snap = First point
cam\x = 0.01
cam\y = 0.01
;draw(R)
;WaitKey
i = 0
While i < q
i = i + 1
center = queue[i]
angoff# = ao[i]
For j = 1 To n-1 ;skips origin point
Local nXY#[2]
ang# = (j*theta + angoff) Mod 360
x2# = rad*Cos(ang)
y2# = rad*Sin(ang)
translate(x2,y2, -center\x,-center\y, nXY)
coincide = 0
For k = 1 To q
If KeyHit(1) End
p2 = queue[k]
If Abs(p2\x - nXY[1]) < tolerance And Abs(p2\y - nXY[2]) < tolerance
center\numLinks = center\numLinks + 1
center\links[ center\numLinks ] = p2
coincide = 1
Exit
EndIf
Next
If coincide = 0 And q < limit And (nXY[1]^2+nXY[2]^2) < distanceLimit
np = createPoint(nXY[1],nXY[2])
np\numLinks = 1
np\links[1] = center
Local offXY#[2]
translate(center\x,center\y, np\x,np\y, offXY)
q = q+1
queue[q] = np
ao[q] = ATan2(offXY[2],offXY[1])
; DebugLog "Point created! "+q
EndIf
; If q > limit
; Return
; EndIf
;draw(R)
;WaitKey
If KeyDown(28) Return
Next
Wend
Local bounds.point[100]
off# = 0.5*(1 - n Mod 2)
;create boundary lines
For i = 0 To n-1
;createPoint(dis*Cos(90+b*theta),dis*Sin(90+b*theta), 255,0,0, 1)
b.boundary = New boundary
b\x1 = dis*Cos(90+(i+off)*theta)
b\y1 = dis*Sin(90+(i+off)*theta)
b\x2 = dis*Cos(90+(i+1+off)*theta)
b\y2 = dis*Sin(90+(i+1+off)*theta)
;b1.point = createPoint(b\x1,b\y1, 255,0,0, 1)
;b2.point = createPoint(b\x2,b\y2, 255,0,0, 1)
;b1\numLinks = 1
;b1\links[1] = b2
If i = 0
r = 255: g=0: bl=0
ElseIf i = 1
r = 0: g=255: bl=0
ElseIf i = 2
r = 0: g=0: bl=255
Else
r = 255: g=0: bl=255
EndIf
bounds[i+1] = createPoint(b\x1,b\y1, r,g,bl, 1)
bounds[i+1]\numLinks = 1
If i > 0
bounds[i+1]\links[1] = bounds[i]
EndIf
Next
bounds[1]\links[1] = bounds[n]
End Function
Function createPoint.point(x#,y#, r=255,g=255,b=255, show=0, toDelete=0)
p.point = New point
p\x = x
p\y = y
p\u = transform(p\x,p\y, 1)
p\v = transform(p\x,p\y, 2)
lastPoint.point = Last point
p\id = lastPoint\id + 1
p\r = r
p\g = g
p\b = b
p\show = show
p\toDelete = toDelete
Return p
End Function
Function getInput(R)
active = 0
mx = MouseX()
my = MouseY()
mkey = 0
cam.camera = First camera
tx# = 0
ty# = 0
scrollSpeed# = 0.10
k# = cosh(scrollSpeed)
mult = -(2*cam\yparity - 1)
If KeyDown(32) Or KeyDown(205)
tx = -scrollSpeed ;* mult
ElseIf KeyDown(30) Or KeyDown(203)
tx = scrollSpeed ;* mult
EndIf
If KeyDown(17) Or KeyDown(200)
ty = -scrollSpeed * mult
ElseIf KeyDown(31) Or KeyDown(208)
ty = scrollSpeed * mult
EndIf
If KeyHit(49)
;Stop
If cam\snap = First point
cam\snap = Last point
Else
cam\snap = Before cam\snap
EndIf
cam\x = cam\snap\x
cam\y = cam\snap\y
active = 1
ElseIf KeyHit(50)
If cam\snap = Last point
cam\snap = First point
Else
cam\snap = After cam\snap
EndIf
cam\x = cam\snap\x
cam\y = cam\snap\y
active = 1
EndIf
If KeyDown(16)
cam\orient = (cam\orient + 5*mult + 360) Mod 360
cam\vorient = (cam\vorient + 5) Mod 360
active = 1
ElseIf KeyDown(18)
cam\orient = (cam\orient - 5*mult + 360) Mod 360
cam\vorient = (cam\vorient - 5 + 360) Mod 360
active = 1
EndIf
If tx <> 0 Or ty <> 0
d# = Sqr(tx*tx + ty*ty)
ang# = ATan2(ty,tx)
cam\vx = offsetStep(cam\vx,cam\vy, d,ang+cam\vorient, 1)
cam\vy = offsetStep(cam\vx,cam\vy, d,ang+cam\vorient, 2)
nx# = offsetStep(cam\x,cam\y, d,ang+1*cam\orient, 1)
ny# = offsetStep(cam\x,cam\y, d,ang+1*cam\orient, 2)
Local out#[2]
tempx# = 0
tempy# = 0
intX# = 0
intY# = 0
done = 0
crossed.boundary = Null
pick.boundary = Null
iters = 0
;DebugLog "cam\x = "+cam\x+", cam\y = "+cam\y
;DebugLog "nx = "+nx+", ny = "+ny
While Not done
done = 1
max# = 10000
pick = Null
;DebugLog iters
For b.boundary = Each boundary
If b <> crossed
intersection(b\x1,b\y1, b\x2,b\y2, cam\x,cam\y, nx,ny, out)
If out[0] = 1 ;there was an intersection
;out[1] = -out[1]
;createPoint(out[1],out[2], 0,255,255, 1,1)
done = 0
d# = hyperD(out[1],out[2], cam\x,cam\y)
;DebugLog "d = "+d
If d < max
max = d
pick = b
; DebugLog "pick: "+Str(pick)
EndIf
EndIf
EndIf
Next
If Not done
intersection(pick\x1,pick\y1, pick\x2,pick\y2, cam\x,cam\y, nx,ny, out)
;out[1] = -out[1]
;createPoint(out[1],out[2], 0,255,0, 1,1)
iters = iters + 1
;DebugLog " (intersection) out[1] = "+out[1]+", out[2] = "+out[2]
cam\x = out[1]
cam\y = out[2]
;ang1# = hyperAng(cam\x,cam\y, nx,ny)
flipOverLine(nx,ny, pick\x1,pick\y1, pick\x2,pick\y2, out)
;createPoint(out[1],out[2], 255,255,0, 1,1)
;DebugLog " (reflection) out[1] = "+out[1]+", out[2] = "+out[2]
nx = out[1]
ny = out[2]
;ang2# = hyperAng(cam\x,cam\y, nx,ny)
ang3# = hyperAng(cam\x,cam\y, pick\x1,pick\y1)
;DebugLog Str(pick)
;DebugLog "cam\orient = "+cam\orient
;DebugLog "ang3 = "+ang3
angdiff# = ang3 - (cam\orient) ;( (ang3 - cam\orient) + 180) Mod 360 - 180
;DebugLog "angdiff = "+angdiff
cam\orient = (cam\orient + (2* angdiff) + 3600) Mod 360
;DebugLog "new cam\orient = "+cam\orient
cam\yparity = Not cam\yparity
crossed = pick
;DebugLog ""
;If iters > 2
;DebugLog "Wah!"
;DebugLog ""
;Exit
;EndIf
EndIf
Wend
If iters > 0
FlushKeys
EndIf
cam\x = nx
cam\y = ny
; Local newXY#[2]
; translate(cam\x,cam\y, -offX,-offY, newXY)
; cam\x = newXY[1]
; cam\y = newXY[2]
active = 1
EndIf
; mouseMoving = (MouseXSpeed() Or MouseYSpeed())
;
; mbutton = 0
; If (MouseDown(1) And mouseMoving) Or MouseHit(1)
; mbutton = 1
; ElseIf (MouseDown(2) And mouseMoving) Or MouseHit(2)
; mbutton = 2
; EndIf
;
; If mbutton > 0
; u1# = (mx-GraphicsWidth()/2.)/R
; v1# = (my-GraphicsHeight()/2.)/R
;
; x1# = invTransform(u1,v1,1)
; y1# = invTransform(u1,v1,2)
;
; Local tXY#[2]
; translate(-x1,y1, -cam\x,-cam\y, tXY)
;
; p.point = Last point
; While p <> First point And p\mouseControlled <> mbutton
; p = Before p
; Wend
;
; p\x = tXY[1]
; p\y = tXY[2]
;
; ;DebugLog tXY[1]+", "+tXY[2]
;
; active = 1
; EndIf
;If MouseXSpeed() Or MouseYSpeed() Return 1
Return active
End Function
Function draw(R)
gw = GraphicsWidth()
gh = GraphicsHeight()
Color 255,255,255
circ(gw/2,gh/2, R, 0)
cam.camera = First camera
For p.point = Each point
If KeyHit(57) Stop
Local tXY#[2]
translate(p\x,p\y, cam\x,cam\y, tXY)
mult = 1 - 2*cam\yparity
tu# = -transform(tXY[1],tXY[2], 1)
tv# = mult * transform(tXY[1],tXY[2], 2)
p\tu = tu*Cos(cam\orient*mult) - tv*Sin(cam\orient*mult)
p\tv = tu*Sin(cam\orient*mult) + tv*Cos(cam\orient*mult)
If p\show
Color p\r,p\g,p\b
circ(R*p\tu+gw/2,R*p\tv+gh/2, 3, 1)
EndIf
If p\toDelete
Delete p
EndIf
Next
Local vals#[3]
For p1.point = Each point
For idx = 1 To p1\numlinks
p2.point = p1\links[idx]
u1# = p1\tu
v1# = p1\tv
u2# = p2\tu
v2# = p2\tv
denom# = u1*v2-u2*v1
If KeyHit(57) And Abs(p1\x) < 0.1 And Abs(p1\y) = 0.1
Stop
EndIf
If Abs(denom) < 0.001
Color 255,255,255
p1tx = R * p1\tu + gw/2
p1ty = R * p1\tv + gh/2
p2tx = R * p2\tu + gw/2
p2ty = R * p2\tv + gh/2
Line p1tx,p1ty, p2tx,p2ty
Else
f# = (u1*u1+v1*v1+1)/2.
g# = (u2*u2+v2*v2+1)/2.
If Abs(v2) > 0.0001
h# = (v2*f-v1*g)/denom
k# = (g-u2*h)/v2
ElseIf Abs(v1) > 0.0001
h# = (v2*f-v1*g)/denom
k# = (f-u1*h)/v1
Else
Stop
EndIf
rad# = Sqr(h*h+k*k-1)
angMin# = ATan2(v1-k,u1-h)
angMax# = ATan2(v2-k,u2-h)
angDiff# = (angMax-angMin)
If angDiff * 2 <> angDiff
While angDiff < -180 Or angDiff > 180
If angDiff < -180
angDiff = angDiff + 360
Else
angDiff = angDiff - 360
EndIf
Wend
numSteps = 20
angStep# = angDiff/numSteps
Color 255,255,255
For n = 0 To numSteps-1
ang# = angMin + n*angStep
x1 = R*(h+rad*Cos(ang)) + GraphicsWidth()/2
y1 = R*(k+rad*Sin(ang)) + GraphicsHeight()/2
x2 = R*(h+rad*Cos(ang+angStep)) + GraphicsWidth()/2
y2 = R*(k+rad*Sin(ang+angStep)) + GraphicsHeight()/2
Line x1,y1, x2,y2
Next
EndIf
EndIf
;end of line drawing
Next
Next
Color 255,255,0
Line gw/2-2,gh/2, gw/2+2,gh/2
Line gw/2,gh/2-2, gw/2,gh/2+2
End Function
Function plotCoords(x#,y#, r=255,g=255,b=255, rad=300)
cam.camera = First camera
Local out#[2]
translate(x,y, -cam\x,-cam\y, out)
nx# = transform(out[1],out[2],1)*rad + GraphicsWidth()/2
ny# = transform(out[1],out[2],2)*rad + GraphicsHeight()/2
Color r,g,b
circ(nx,ny, 2,1)
End Function
Function offsetStep#(px#,py#, d#,theta#, which)
k# = (Exp(d)+1/Exp(d))/2
If px = 0 And py = 0
r# = Sqr(k*k-1)
If which = 1
Return r*Cos(theta)
Else
Return r*Sin(theta)
EndIf
EndIf
a# = 1 + px^2*Sin(theta)^2 + py^2*Cos(theta)^2 - 2*px*py*Cos(theta)*Sin(theta)
b# = 2*(1-k)*(px*Cos(theta) + py*Sin(theta))
c# = (1 - k*k + 2*(1-k)*(px*px + py*py) )
det# = b*b-4*a*c
rpos# = (-b + Sqr(det))/(2*a)
rneg# = (-b - Sqr(det))/(2*a)
If rpos < 0
temp# = rpos
rpos = rneg
rneg = temp
EndIf
If which = 1
Return px + rpos*Cos(theta)
ElseIf which = 2
Return py + rpos*Sin(theta)
EndIf
End Function
Function translateUV#(pu#,pv#, tu#,tv#, which) ;(pu,pv) = point to translate, (tu,tv) = point to move to origin
vdotx# = pu*tu + pv*tv ;tu*p\u + tv*p\v
mag2v# = tu*tu + tv*tv ;tu*tu + tv*tv
mag2x# = pu*pu + pv*pv ;p\u*p\u + p\v*p\v
If which = 1
Return ( (1.+2*vdotx+mag2x)*tu + (1.-mag2v)*pu ) / (1. + 2*vdotx + mag2v*mag2x)
ElseIf which = 2
Return ( (1.+2*vdotx+mag2x)*tv + (1.-mag2v)*pv ) / (1. + 2*vdotx + mag2v*mag2x)
EndIf
End Function
Function translate#(px#,py#, tx#,ty#, out#[2]) ;tx,ty to origin
pt# = Sqr(1.+px*px+py*py)
tt# = Sqr(1.+tx*tx+ty*ty)
If tx = 0 And ty = 0
out[1] = px
out[2] = py
Return
EndIf
x1# = tt
x2# = tx
x3# = ty
a# = x1
d# = -x2
g# = -x3
b# = -x2
c# = -x3
f# = (x1*x2*x3 - (x2*x3))/(x2*x2+x3*x3)
h# = f
e# = (x1*x2*x2 + x3*x3)/(x2*x2+x3*x3)
i# = (x1*x3*x3 + x2*x2)/(x2*x2+x3*x3)
;matrix is done!
nt# = a*pt + b*px + c*py
nx# = d*pt + e*px + f*py
ny# = g*pt + h*px + i*py
out[0] = nt
out[1] = nx
out[2] = ny
Return
End Function
Function translatePoint(p.point, tx#,ty#)
Local out#[2]
translate(p\x,p\y, tx,ty, out)
p\x = out[1]
p\y = out[2]
End Function
Function transform#(x#,y#, which)
;If x*x+y*y > 1
; Return -1
;EndIf
t# = Sqr(1+x*x+y*y)
If which = 1
Return x/(1.+t)
ElseIf which = 2
Return y/(1.+t)
EndIf
End Function
Function invTransform#(u#,v#, which)
denom# = 1.-u*u-v*v
If which = 1
Return 2.*u/denom
ElseIf which = 2
Return 2.*v/denom
EndIf
End Function
Function polygon(centerX#,centerY#, dis#, sides, angoffset#)
angstep# = 360./sides
rad# = cosh(dis)
prevPoint.point = Last point
idStart = prevPoint\id
prevPoint = Null
begPoint.point = Null
; centerU# = transform(centerX,centerY, 1)
; centerV# = transform(centerX,centerY, 2)
For i = 0 To sides-1
p.point = New point
;tempx# = offsetStep(0,0, rad, i*angstep + angoffset, 1)
;tempy# = offsetStep(0,0, rad, i*angstep + angoffset, 2)
tempx# = rad*Cos(i*angstep + angoffset)
tempy# = rad*Sin(i*angstep + angoffset)
Local newXY#[2]
translate(tempx,tempy, -centerX,-centerY, newXY)
p\x = newXY[1]
p\y = newXY[2]
p\r = 255
p\g = 255
p\b = 255
p\id = idStart + 1
idStart = idStart + 1
;If begPoint <> Null
; begPoint = p
;EndIf
If prevPoint <> Null
prevPoint\links[1] = p
prevPoint\numLinks = 1
EndIf
prevPoint = p
Next
prevPoint\numLinks = 1
For j = 1 To sides-1
p = Before p
Next
prevPoint\links[1] = p
p\r = 255
p\g = 0
p\b = 0
End Function
Function polygon_oriented(centerX#,centerY#, orientX#,orientY#, dis#, sides)
angstep# = 360./sides
rad# = dis;cosh(dis)
prevPoint.point = Last point
idStart = prevPoint\id
prevPoint = Null
begPoint.point = Null
; centerU# = transform(centerX,centerY, 1)
; centerV# = transform(centerX,centerY, 2)
Local orientT_XY#[2]
translate(orientX,orientY, -centerX,-centerY, orientT_XY)
angoffset# = (ATan2(orientT_XY[2], orientT_XY[1]) + 180*((sides+0) Mod 2)) Mod 360
For i = 0 To sides-1
p.point = New point
;tempx# = offsetStep(0,0, rad, i*angstep + angoffset, 1)
;tempy# = offsetStep(0,0, rad, i*angstep + angoffset, 2)
tempx# = rad*Cos(i*angstep + angoffset)
tempy# = rad*Sin(i*angstep + angoffset)
Local newXY#[2]
translate(tempx,tempy, -centerX,-centerY, newXY)
p\x = newXY[1]
p\y = newXY[2]
p\r = 255
p\g = 255
p\b = 255
p\id = idStart + 1
idStart = idStart + 1
;If begPoint <> Null
; begPoint = p
;EndIf
If prevPoint <> Null
prevPoint\links[1] = p
prevPoint\numLinks = 1
EndIf
prevPoint = p
Next
prevPoint\numLinks = 1
For j = 1 To sides-1
p = Before p
Next
prevPoint\links[1] = p
p\r = 255
p\g = 0
p\b = 0
End Function
Function polygon_old(centerX#,centerY#, rad#, sides, angoffset#)
angstep# = 360./sides
prevPoint.point = Last point
idStart = prevPoint\id
prevPoint = Null
begPoint.point = Null
centerU# = transform(centerX,centerY, 1)
centerV# = transform(centerX,centerY, 2)
For i = 0 To sides-1
p.point = New point
tempx# = offsetStep(0,0, rad, i*angstep + angoffset, 1)
tempy# = offsetStep(0,0, rad, i*angstep + angoffset, 2)
; p\x = tempx ;translateUV(tempx,tempy, -centerX,-centerY, 1)
; p\y = tempy ;translateUV(tempx,tempy, -centerX,-centerY, 2)
tempu# = transform(tempx,tempy, 1)
tempv# = transform(tempx,tempy, 2)
p\u = translateUV(tempu,tempv, centerU,centerV, 1)
p\v = translateUV(tempu,tempv, centerU,centerV, 2)
p\x = invTransform(p\u,p\v, 1)
p\y = invTransform(p\u,p\v, 2)
p\r = 255
p\g = 255
p\b = 255
p\id = idStart + 1
idStart = idStart + 1
;If begPoint <> Null
; begPoint = p
;EndIf
If prevPoint <> Null
prevPoint\links[1] = p
prevPoint\numLinks = 1
EndIf
prevPoint = p
Next
prevPoint\numLinks = 1
For j = 1 To sides-1
p = Before p
Next
prevPoint\links[1] = p
End Function
Function intersection(x1#,y1#, x2#,y2#, u1#,v1#, u2#,v2#, XY#[2], strict=1, debug=0) ;strict checks the line >segments<
;XY[0] will be used to store failure (0) or success (1)
XY[0] = 0
If (x1 = u1 And y1 = v1 And x2 = u2 And y2 = v2) Or (x1 = u2 And y1 = v2 And x2 = u1 And y2 = v1)
Return
EndIf
If debug = 1
DebugLog "---------------------"
DebugLog "Original coordinates:"
DebugLog " x1 = "+x1+", y1 = "+y1
DebugLog " x2 = "+x2+", y2 = "+y2
DebugLog " u1 = "+u1+", v1 = "+v1
DebugLog " u2 = "+u2+", v2 = "+v2
DebugLog ""
EndIf
Local tXY_1#[2]
Local tXY_2#[2]
Local tXY_3#[2]
translate(x2,y2, x1,y1, tXY_1) ;translate all points so that (x1,y1) = (0,0)
translate(u1,v1, x1,y1, tXY_2)
translate(u2,v2, x1,y1, tXY_3)
If debug = 1
DebugLog "Translated coordinates:"
DebugLog " tXY_1[1] = "+tXY_1[1]+", tXY_1[2] = "+tXY_1[2]
DebugLog " tXY_2[1] = "+tXY_2[1]+", tXY_2[2] = "+tXY_2[2]
DebugLog " tXY_3[1] = "+tXY_3[1]+", tXY_3[2] = "+tXY_3[2]
DebugLog ""
EndIf
ang# = ATan2(tXY_1[2],tXY_1[1]) ;calculate angle to (x2,y2)
tU1# = tXY_2[1]*Cos(-ang) - tXY_2[2]*Sin(-ang) ;rotate (u1,v1) by -ang
tV1# = tXY_2[1]*Sin(-ang) + tXY_2[2]*Cos(-ang)
tU2# = tXY_3[1]*Cos(-ang) - tXY_3[2]*Sin(-ang) ;rotate (u2,v2) by -ang
tV2# = tXY_3[1]*Sin(-ang) + tXY_3[2]*Cos(-ang)
If debug = 1
DebugLog "Rotated coordinates (rotated by "+ang+" degrees):"
DebugLog " tU1 = "+tU1+", tV1 = "+tV1
DebugLog " tU2 = "+tU2+", tV2 = "+tV2
DebugLog ""
EndIf
s# = tU1
t# = tV1
u# = tU2
v# = tV2
tst# = Sqr(1 + s*s + t*t)
tuv# = Sqr(1 + u*u + v*v)
p# = s*v - u*t
q# = t*tuv - v*tst
If q*q - p*p <= 0 Return
;tk# = Abs(q)*Sqr( 1/(q*q - p*p) )
k# = -p*Sgn(q)/Sqr(q*q-p*p)
If debug = 1
DebugLog "Solution: k = "+k
EndIf
;intersection point is at (k,0)
kX# = k*Cos(ang) ;rotate solution by ang
kY# = k*Sin(ang)
translate(kX,kY, -x1,-y1, XY) ;translate (0,0) to (x1,y1)
; XY[1] = -XY[1] ;I don't really know WHY
If debug = 1
DebugLog "Final solution:"
DebugLog " XY[1] = "+XY[1]+", XY[2] = "+XY[2]
DebugLog ""
EndIf