Rotating Globe

[Petr]

Hi. This program was created in collaboration. I was interested in it. By modifying the scale, you can zoom in and out on the textured sphere. The whole thing is created using 2D commands, instead of PSet I used _MapTriangle (in the 2D version) because you write here that you want to rotate the sphere and you don't write anything about approaching it with jumps. There was a problem with the fact that the back and front parts were redrawn, so you had to determine which part was visible and only that was drawn. I left Czech and English comments in the program, because I'm sure I'll come back to it.

Code: (Select All)

' Rotující texturovaná koule vykreslená pomocí _MAPTRIANGLE s backface culling

' (Rotating textured sphere rendered using _MAPTRIANGLE with backface culling)



Screen _NewImage(800, 600, 32)

myTexture = _LoadImage("6.jpg")

If myTexture = 0 Then

    Print "Can not load '6.jpg'!"

    End

End If



texWidth = _Width(myTexture)

texHeight = _Height(myTexture)

' (Obtaining the width and height of the loaded texture)



Const PI = 3.14159265

Const centerX = 400 ' Střed obrazovky (X)  Screen middle X

Const centerY = 300 ' Střed obrazovky (Y)  Screen middle Y

Const scale = 200 ' Měřítko projekce        Projection ratio

' (Define constants for PI, screen center coordinates, and the projection scale)



' Nastavení rozlišení sítě (kolik segmentů se použije)

' (Setting the mesh resolution - how many segments to use)

Const nPhi = 40 ' Počet dělení kolem osy (azimut)                Number of divisions around the axis (azimuth)

Const nTheta = 20 ' Počet dělení od pólu k pólu (polární úhel)  Number of divisions from pole to pole (polar angle)

Dim stepPhi As Single, stepTheta As Single

stepPhi = 360 / nPhi

stepTheta = 180 / nTheta

' (Calculates the angular step sizes for phi (azimuth) and theta (polar angle))



' (User Defined Type with additional fields for 3D coordinates used for backface culling)

Type Vertex

    sx As Integer ' Projekční X na obrazovce            Projection X on screen

    sy As Integer ' Projekční Y na obrazovce            Projection Y on screen

    u As Single ' Texturovací souřadnice U (0 až 1)      Texturing coordinate U 0 to 1

    v As Single ' Texturovací souřadnice V (0 až 1)      Texturing coordinate V 0 to 1

    x3d As Single ' Otočená 3D souřadnice X              rotation 3D X

    y3d As Single ' Otočená 3D souřadnice Y              rotation 3D Y

    z3d As Single ' Otočená 3D souřadnice Z              rotation 3D Z

End Type

' (The Vertex type stores both the 2D projected coordinates (sx, sy) and the texture coordinates (u, v),

'  as well as the transformed 3D coordinates (x3d, y3d, z3d) for performing backface culling)



' Globální rotační úhly (v°)

' (Global rotation angles in degrees)

Dim rotationX As Single, rotationY As Single

rotationX = 0

rotationY = 0



Do

    ' Používáme původní _KeyDown hodnoty

    ' (Using the original _KeyDown key codes)

    If _KeyDown(18432) Then rotationX = rotationX - 5 ' Šipka vlevo (Left arrow decreases rotationX)

    If _KeyDown(20480) Then rotationX = rotationX + 5 ' Šipka vpravo (Right arrow increases rotationX)

    If _KeyDown(19200) Then rotationY = rotationY - 5 ' Šipka nahoru (Up arrow decreases rotationY)

    If _KeyDown(19712) Then rotationY = rotationY + 5 ' Šipka dolů (Down arrow increases rotationY)



    Cls , 0

    _PrintString (0, 0), "Rotující texturovaná koule s backface culling"

    _PrintString (0, 16), "Použijte šipky. ESC pro ukončení."

    _PrintString (0, 32), "rotationX = " + Str$(rotationX) + "  rotationY = " + Str$(rotationY)

    ' (Clears the screen and prints the title and current rotation angles for debugging)



    Dim i As Integer, j As Integer

    Dim phi1 As Single, phi2 As Single, theta1 As Single, theta2 As Single

    Dim v1 As Vertex, v2 As Vertex, v3 As Vertex, v4 As Vertex



    ' Procházení sférickou sítí – každý segment (čtverec) rozdělíme na 2 trojúhelníky

    ' (Loop through the spherical mesh; each quad (square) is divided into 2 triangles)

    For i = 0 To nPhi - 1

        For j = 0 To nTheta - 1

            phi1 = i * stepPhi

            phi2 = (i + 1) * stepPhi

            If phi2 >= 360 Then phi2 = phi2 - 360

            theta1 = j * stepTheta

            theta2 = (j + 1) * stepTheta



            ' Výpočet vrcholů segmentu – předáváme aktuální hodnoty rotace

            ' (Calculate the vertices of the segment, passing the current rotation values)

            GetVertex v1, phi1, theta1, rotationX, rotationY

            GetVertex v2, phi2, theta1, rotationX, rotationY

            GetVertex v3, phi1, theta2, rotationX, rotationY

            GetVertex v4, phi2, theta2, rotationX, rotationY



            ' Vykreslíme pouze trojúhelníky, které jsou "front-facing"

            ' (Render only the triangles that are front-facing)

            If IsFrontFace(v1, v2, v3) Then

                _MapTriangle (v1.u * texWidth, v1.v * texHeight)-(v2.u * texWidth, v2.v * texHeight)-(v3.u * texWidth, v3.v * texHeight), myTexture To(v1.sx, v1.sy)-(v2.sx, v2.sy)-(v3.sx, v3.sy), _Smooth

            End If

            If IsFrontFace(v2, v4, v3) Then

                _MapTriangle (v2.u * texWidth, v2.v * texHeight)-(v4.u * texWidth, v4.v * texHeight)-(v3.u * texWidth, v3.v * texHeight), myTexture To(v2.sx, v2.sy)-(v4.sx, v4.sy)-(v3.sx, v3.sy), _Smooth

            End If

        Next j

    Next i



    _Display

Loop Until _KeyDown(27) ' ESC ukončí program

' (The main loop continues until the ESC key is pressed)



'------------------------------------------------------

' SUB GetVertex

'

' Vstup:

'  phi, theta: sférické úhly (v°)

'  rotX, rotY: aktuální hodnoty rotace (v°), předané z hlavního programu

'

' Výstup (v):

'  v.sx, v.sy: 2D projekční souřadnice

'  v.u, v.v: texturovací souřadnice (v rozsahu 0 až 1)

'  v.x3d, v.y3d, v.z3d: otočené 3D souřadnice (pro backface culling)

'

' Postup:

'  1. Vypočítá se původní (neotočený) bod na jednotkové kouli:

'        x0 = sin(theta)*cos(phi)

'        y0 = cos(theta)

'        z0 = sin(theta)*sin(phi)

'  2. Z tohoto bodu se spočítají texturovací souřadnice:

'        u = (ATAN2(z0, x0) + PI) / (2*PI)

'        v = ACOS(y0) / PI

'  3. Následně se na původní bod aplikuje rotace – nejprve kolem osy Y, potom kolem osy X.

'  4. Výsledek se uloží do v.x3d, v.y3d, v.z3d a podle něj se spočítají 2D projekční souřadnice.

'

' Input:

' phi, theta: spherical angles (v°)

' rotX, rotY: current rotation values ??(v°), passed from the main program

'

' Output (v):

' v.sx, v.sy: 2D projection coordinates

' v.u, v.v: texturing coordinates (in the range 0 to 1)

' v.x3d, v.y3d, v.z3d: rotated 3D coordinates (for backface culling)

'

' Procedure:

' 1. The original (unrotated) point on the unit sphere is calculated:

' x0 = sin(theta)*cos(phi)

' y0 = cos(theta)

' z0 = sin(theta)*sin(phi)

' 2. The texturing coordinates are calculated from this point:

' u = (ATAN2(z0, x0) + PI) / (2*PI)

' v = ACOS(y0) / PI

' 3. Subsequently, on the original point is rotated – first around the Y axis, then around the X axis.

' 4. The result is stored in v.x3d, v.y3d, v.z3d and the 2D projection coordinates are calculated based on it.



' (SUB GetVertex calculates the vertex data for a given spherical coordinate.

'  It computes the original (unrotated) point on the unit sphere, derives the texture coordinates,

'  then applies rotation (first around the Y-axis, then around the X-axis) and computes the 2D projection.)

'------------------------------------------------------

Sub GetVertex (v As Vertex, phi As Single, theta As Single, rotX As Single, rotY As Single)

    Dim radPhi As Single, radTheta As Single

    radPhi = phi * (PI / 180)

    radTheta = theta * (PI / 180)



    ' Původní (neotočený) bod na jednotkové kouli

    ' (Calculate the original, unrotated point on the unit sphere)

    Dim x0 As Single, y0 As Single, z0 As Single

    x0 = Sin(radTheta) * Cos(radPhi)

    y0 = Cos(radTheta)

    z0 = Sin(radTheta) * Sin(radPhi)



    ' Výpočet texturovacích souřadnic (z neotočeného bodu)

    ' (Calculate texture coordinates from the unrotated point)

    v.u = (_Atan2(z0, x0) + PI) / (2 * PI)

    v.v = _Acos(y0) / PI



    ' Inicializace – budeme transformovat původní bod

    ' (Initialize transformation with the original point)

    Dim x As Single, y As Single, z As Single

    x = x0: y = y0: z = z0



    ' Nejprve rotace kolem osy Y (vertikální rotace)

    ' (Apply rotation around the Y-axis first - vertical rotation)

    Dim ry As Single

    ry = rotY * (PI / 180)

    Dim xtemp As Single, ztemp As Single

    xtemp = x * Cos(ry) + z * Sin(ry)

    ztemp = -x * Sin(ry) + z * Cos(ry)

    x = xtemp: z = ztemp



    ' Poté rotace kolem osy X (horizontální rotace)

    ' (Then apply rotation around the X-axis - horizontal rotation)

    Dim rx As Single

    rx = rotX * (PI / 180)

    Dim ytemp As Single

    ytemp = y * Cos(rx) - z * Sin(rx)

    ztemp = y * Sin(rx) + z * Cos(rx)

    y = ytemp: z = ztemp



    ' Uložení otočených 3D souřadnic do vrcholu (pro pozdější backface culling)

    ' (Store the rotated 3D coordinates in the vertex for later backface culling)

    v.x3d = x

    v.y3d = y

    v.z3d = z



    ' Projekce do 2D (ortografická)

    ' (Calculate the 2D orthographic projection)

    v.sx = centerX + x * scale

    v.sy = centerY - y * scale

End Sub



'------------------------------------------------------

' Funkce IsFrontFace

'

' Vstup: tři vrcholy trojúhelníku (v1, v2, v3) se svými 3D souřadnicemi.

' Výpočet: spočítá se normála trojúhelníku a poté její dot produkt s vektorem pohledu (0,0,-1).

' Pokud je výsledek > 0 (tj. normála směřuje ke kameře), vrátí funkce true.

' V našem případě (s ortografickou projekcí a kamerou směřující do -Z)

' platí: pokud normála má složku z menší než 0, trojúhelník je viditelný.

'

' (Function IsFrontFace determines whether a triangle is facing the camera.

'  It calculates the cross product (normal) of two edges of the triangle and uses its Z-component,

'  comparing it with the view vector (0,0,-1). If the condition is met (normal's Z-component < 0),

'  the triangle is considered front-facing.)

'------------------------------------------------------

Function IsFrontFace (v1 As Vertex, v2 As Vertex, v3 As Vertex)

    Dim edge1_x As Single, edge1_y As Single, edge1_z As Single

    Dim edge2_x As Single, edge2_y As Single, edge2_z As Single

    edge1_x = v2.x3d - v1.x3d

    edge1_y = v2.y3d - v1.y3d

    edge1_z = v2.z3d - v1.z3d

    edge2_x = v3.x3d - v1.x3d

    edge2_y = v3.y3d - v1.y3d

    edge2_z = v3.z3d - v1.z3d

    ' Vypočítáme pouze složku Z normály (cross product)

    ' (Compute only the Z component of the normal via cross product)

    Dim norm_z As Single

    norm_z = edge1_x * edge2_y - edge1_y * edge2_x

    ' Pohled: vektor (0,0,-1). Dot produkt = -norm_z.

    ' Trojúhelník je front-facing, pokud -norm_z > 0  <=>  norm_z < 0.

    ' (With the view vector (0,0,-1), the dot product is -norm_z.

    '  The triangle is considered front-facing if -norm_z > 0, i.e., if norm_z < 0.)

    If norm_z < 0 Then

        IsFrontFace = -1

    Else

        IsFrontFace = 0

    End If

End Function