Mystery Curve

Mystery Curve article here:
http://www.johndcook.com/blog/2015/06/03/mystery-curve/
he provides formula Exp(it) – Exp(6it)/2 + i Exp(-14it)/3 , for t going to 2*pi and i is the imaginary number, he provides a python code using numby math library
i see thinbasic have complex numbers functions, but until i find a way to use these functions in this context, i have resorted to wolfram alpha to simplify the formula, interestingly they recognize i as imaginary:
simplify Exp(it) – Exp(6it)/2 + i Exp(-14it)/3
fortunately they provide this simplification
1/3 sin(14 t)+cos(t)-1/2 cos(6 t)+ i (sin(t)-1/2 sin(6 t)+1/3 cos(14 t))
note that wolframAlpha is too advanced and have something like A.I.
so what comes after i we assign to y, and what come first we assign to x
x = Cos(t) - Cos(6* t)/2 + Sin(14* t)/3
y = Cos(14* t)/3 + Sin(t)- Sin(6* t)/2
z : for the fun only , give it a value of 0 or 1 to get a stereo scene z = Rnd(0,1), or give it a value z = 0 to get one curve.
in fact i have used older code (shark equation), the only trouble is in simplifying the Mystery curve formula.
hope this page is of value to who may have trouble in plotting Exp(it) – Exp(6it)/2 + i Exp(-14it)/3
Attachment 9604

Code:

Uses "TBGL" Uses "math" Function TBMain() Local hWnd As DWord Local FrameRate As Double ' -- Create and show window hWnd = TBGL_CreateWindowEx("Mystery Curve using GBuffers - press ESC to quit", 600, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX) TBGL_ShowWindow TBGL_BackColor 255,255,255 TBGL_SetDrawDistance 250 ' -- Create 3D points buffer Dim gbPoints As DWord = TBGL_GBufferCreate(%TBGL_POINTS, %TBGL_3D) 'Dim gbPoints As DWord = TBGL_GBufferCreate(%TBGL_LINES, %TBGL_3D) Global Nb As DWord = 30159 '10053 '30159 '62831 ' -- Define data for it Global VertexA(Nb) As TBGL_TVECTOR3F Global ColorA(Nb) As TBGL_TRGB FillArrays ' call the sub to fill VertexA , ColorA arrays ' -- Create buffer dynamically linked to the arrays above TBGL_GBufferDefineFromArray(gbPoints, %TBGL_DYNAMIC, CountOf(VertexA), VertexA(1), ColorA(1)) ' -- Resets status of all keys TBGL_ResetKeyState() 'TBGL_PointSize 2 'if you want thick points uncomment this line ' -- Main loop While TBGL_IsWindow(hWnd) 'init FrameRate = TBGL_GetFrameRate TBGL_ClearFrame TBGL_Camera(0, 0, 50, 0, 0, 0) ' -- Turn triangle TBGL_Rotate GetTickCount/50, 0, 1, 0 'TBGL_Scale 0.6, 0.6, 0.6 ' -- Render it TBGL_GBufferRender(gbPoints) TBGL_DrawFrame ' -- ESCAPE key to exit application If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While Wend ' -- Destroying the buffer is not necessary, ' -- the garbage collector will take care of it ' -- Destroy window TBGL_DestroyWindow End Function Sub FillArrays() Dim x, y, z, t As Single Dim N As DWord = 1 While t <= 2*Pi 'Exp(it) – Exp(6it)/2 + i Exp(-14it)/3 x = Cos(t) - Cos(6* t)/2 + Sin(14* t)/3 y = Cos(14* t)/3 + Sin(t)- Sin(6* t)/2 z = Rnd(0,1) VertexA(N).x = x*6 VertexA(N).y = y*6 VertexA(N).z = z*3 'ColorA(N).r = 255 :ColorA(N).g = 0 :ColorA(N).b = 0 If z = 1 Then ColorA(N).r = 255 :ColorA(N).g = 0 :ColorA(N).b = 0 Else ColorA(N).r = 0 :ColorA(N).g = 0 :ColorA(N).b = 255 End If t + 0.0003 : N + 1 Wend End Sub