Render natively in Poincaré.

gyro.py

@@ -3,6 +3,10 @@ try:
 except ImportError:
     from numpy import complex128 as complex256 
 
+from cmath import sqrt
+from math import tanh, atanh
+from lines import cLineIntersection
+
 def ZeroCheck(cN):
     if cN == complex256(complex(0,0)):
         return complex256(complex(1,0))
@@ -21,6 +25,9 @@ def cDot(cA, cB):
 def cDist(cA, cB):
     return abs(cA-cB)
 
+def MobiusInt(cA,cB,cC,cD): # Bruh
+    return Klein2Poincare(cLineIntersection(Poincare2Klein(cA),Poincare2Klein(cB),Poincare2Klein(cC),Poincare2Klein(cD)))
+
 def MobiusAdd(cA, cB):
     return (cA + cB) / (1 + cA.conjugate() * cB)
 
@@ -30,9 +37,32 @@ def MobiusGyr(cA, cB):
 def MobiusAddGyr(cA, cB):
     return MobiusAdd(cA, cB), MobiusGyr(cA, cB)
 
+def MobiusScalar(cA, rT):
+    m = abs(cA)
+    return tanh(rT * atanh(m)) * cA / m
+
+def MobiusCoadd(cA,cB):
+    return MobiusAdd(cA, (MobiusGyr(cA,-cB) * cB))
+
+def MobiusCosub(cA,cB):
+    return MobiusAdd(cA, -(MobiusGyr(cA,cB) * cB))
+
+def MobiusLine(cA,cB,rT):
+    return MobiusAdd(
+            cA,
+            MobiusScalar(
+                MobiusAdd(-cA,cB),
+                rT))
+
+def MobiusDist(cA,cB):
+    return abs(MobiusAdd(-cB,cA))
+
 def Poincare2Klein(cN):
     return 2*cN / (1 + cDot(cN,cN))
 
+def Klein2Poincare(cN):
+    return (1-sqrt(1-cDot(cN,cN)))*cN/cDot(cN,cN)
+
 class GyroVector:
     def __init__(self, cPos, cRot):
         self.cPos = complex256(cPos)
@@ -74,3 +104,6 @@ class GyroVector:
     
     def nrtransformed(self, cA):
         return MobiusAdd(self.cPos, cA / self.cRot)
+
+    def dist(self,gA):
+        return abs((-self+gA).cPos)

main.py

@@ -24,6 +24,8 @@ IROT = 1/ROT
 F = 5 * 10**7
 F_ = 10**9
 
+gOrigin = GyroVector(complex256(0),1)
+
 SKY = (127,127,255)
 GROUND = (102, 51, 0)
 
@@ -54,16 +56,16 @@ def draw(level,gPlayer,fov,res):
         m = DrawnSegment(0,BLACK)
         rot = irot**(i-(res/2)) * iprot
         for j in level:
-            tA = Poincare2Klein(MobiusAdd(j.pointA,-gPlayer.cPos))
-            tB = Poincare2Klein(MobiusAdd(j.pointB,-gPlayer.cPos))
-            try: # This function faults from time to time
-                cInt = cLineIntersection(tA,tB,complex256(0),rot)
+            #tA = MobiusAdd(j.pointA,-gPlayer.cPos)
+            #tB = MobiusAdd(j.pointB,-gPlayer.cPos)
+            try: # Function "LineIntersection" faults from time to time
+                cInt = MobiusInt(j.pointA,j.pointB,gPlayer.cPos,rot)
             except ZeroDivisionError:
                 continue
-            rDist = cDist(0,cInt) * irot.real
-            if not (j.isFinite and cBetween(tA,tB,cInt)):
+            if cDot(rot,MobiusAdd(cInt,-gPlayer.cPos)) > 0:
                 continue
-            if cDot(cInt,rot) > 0:
+            rDist = MobiusDist(cInt,gPlayer.cPos)
+            if not (j.isFinite and cBetween(j.pointA,j.pointB,cInt)):
                 continue
             if (1 - m.height) > rDist:
                 m = DrawnSegment(1-rDist,j.color)
@@ -116,13 +118,13 @@ def mainLoop():
 
         display.fill(WHITE)
         #pygame.draw.rect(display,BLACK, c_tr(Poincare2Klein(gPlayer.cPos) * -100) + (100,100),0)
-        drawn = draw(level,gPlayer,PI/2,160)
+        drawn = draw(level,gPlayer,PI/4,320)
         pygame.draw.rect(display,SKY,    (0,0,1280,360))
         pygame.draw.rect(display,GROUND, (0,360,1280,360))
         n = 0
         for i in drawn:
-            pygame.draw.rect(display,i.color, (n,(1 - i.height) * 360,8,cap(i.height) * 1280))
-            n += 8
+            pygame.draw.rect(display,i.color, (n,int((1 - cap(i.height)) * 360),8,int(cap(i.height) * 1280)))
+            n += 4
 
         if debugInfo:
             fps_surf, cPos_surf, cRot_surf = renderDebugInfo(gPlayer, clock, fontSize)