const Xmax = 640 const Ymax = 480 const Xmid = Xmax/2 const Ymid = Ymax/2 const Lens = 256 const PI = 3.141593 const rings = 14 const bands = 15 const ringradius = 100 const bandradius = 40 'x 0 'y 1 'z 2 'screenx 3 'screeny 4 randomize ticks MaxPoint = Rings * Bands dim model(4, MaxPoint-1) '3d points 'p1 0 'p2 1 'p3 2 'index 3 'color 4 dim poly(4, 1) 'polygons LoadTorus Rings, Bands, RINGRADIUS, BandRadius, Model() Tesselate Rings, Bands, Poly() anglex = int(rnd*360) angley = int(rnd*360) anglez = int(rnd*360) cls repeat anglex = (anglex + 1) mod 360 angley = (angley + 1) mod 360 anglez = (anglez + 1) mod 360 RotateAndProject Model(), anglex, angley, anglez DrawModel Model() , Poly() until end '//********************************************************************* SUB DrawModel (byref Model() , byref Poly()) cls FOR I = 0 TO UBOUND(Poly,2) J = Poly(3,I) x1 = Model(3,Poly(0,J)) 'Get triangles from "projected" x2 = Model(3,Poly(1,J)) 'X and Y coords since Znormal x3 = Model(3,Poly(2,J)) 'Does not require a Z coord y1 = Model(4,Poly(0,J)) 'V1= Point1 connected to V2 then y2 = Model(4,Poly(1,J)) 'V2 to V3 and so on... y3 = Model(4,Poly(2,J)) 'Use the Znormal,the Ray perpendicular(Orthogonal) to the Screen 'Defined by the Triangle (X1,Y1,X2,Y2,X3,Y3) 'if Less(<) 0 then its facing in the opposite direction so 'don't plot. If =>0 then its facing towards you so Plot. Znormal = (x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3) c = poly(4,J) IF Znormal >= 0 THEN line x1, y1, x2, y2, color c line x2, y2, x3, y3, color c line x3, y3, x1, y1, color c END IF NEXT I end sub '//********************************************************************* SUB LoadTorus (Rings, Bands, RINGRADIUS, BandRadius, byref Model()) MaxPoint = Rings * Bands A1 = 2 * PI / Rings: A2 = 2 * PI / Bands i = 0 FOR S2 = 0 TO Bands - 1 FOR S1 = 0 TO Rings - 1 X1 = COS(S1 * A1) * RINGRADIUS Y1 = SIN(S1 * A1) * RINGRADIUS Model(0,i) = X1 + COS(S1 * A1) * COS(S2 * A2) * BandRadius Model(1,i) = Y1 + SIN(S1 * A1) * COS(S2 * A2) * BandRadius Model(2,i) = SIN(S2 * A2) * BandRadius i = i + 1 NEXT S1 NEXT S2 end sub '//********************************************************************* SUB RotateAndProject (byref Model(), AngleX, AngleY, AngleZ) ''Right handed system ''when camera components increase: ''x=goes right ''y=goes down ''z goes into the screen '''rotation: counter-clockwise of each axis ''ei. make yourself perpenicular to the axis ''wave your hand from the center of your body to the left. ''That's how it rotates. ;*) 'Precalculate the SIN and COS of each angle ax= anglex*PI/180 ay= angley*PI/180 az= anglez*PI/180 cx = cos(ax) sx = sin(ax) cy = cos(ay) sy = sin(ay) cz = cos(az) sz = sin(az) xx = cy * cz xy = sx * sy * cz - cx * sz xz = cx * sy * cz + sx * sz yx = cy * sz yy = cx * cz + sx * sy * sz yz = -sx * cz + cx * sy * sz zx = -sy zy = sx * cy zz = cx * cy FOR i = 0 TO UBOUND(Model,2) x = Model(0,i) y = Model(1,i) z = Model(2,i) RotX = (x * xx + y * xy + z * xz) RotY = (x * yx + y * yy + z * yz) RotZ = (x * zx + y * zy + z * zz) 'Project Distance = (LENS - RotZ) IF Distance > 0 THEN Model(3,i) = Xmid + (LENS * RotX / Distance) Model(4,i) = Ymid - (LENS * RotY / Distance) ELSE END IF NEXT i END SUB sub Tesselate(Rings, Bands,Byref Poly()) I = 0 MaxTri = 0 FOR S1 = Bands - 1 TO 0 STEP -1 FOR S2 = Rings - 1 TO 0 STEP -1 I = I + 1 MaxTri = MaxTri + 1 I = I + 1 MaxTri = MaxTri + 1 NEXT S2 NEXT S1 REDIM Poly(4,MaxTri) I = 0 FOR S1 = Bands - 1 TO 0 STEP -1 FOR S2 = Rings - 1 TO 0 STEP -1 Poly(0,I) = S1 * Rings + S2 Poly(1,I) = S1 * Rings + (S2 + 1) MOD Rings Poly(2,I) = (S1 * Rings + S2 + Rings) MOD MaxPoint Poly(3,I) = I Poly(4,I) = int(rnd*15) I = I + 1 Poly(0,I) = S1 * Rings + (S2 + 1) MOD Rings Poly(1,I) = (S1 * Rings + (S2 + 1) MOD Rings + Rings) MOD MaxPoint Poly(2,I) = (S1 * Rings + S2 + Rings) MOD MaxPoint Poly(3,I) = I Poly(4,I) = int(rnd*15) I = I + 1 NEXT S2 NEXT S1 end sub