I'm trying to make a circle that has a center in origo. I make this in the GDL programming language. But the problem is actually related to trigonometry.
So I need some help from clever matematics people.
Se the illustration below.
I first put the circle on the horizontal layer (XY-layer and z=0). Center is origo (x=y=z=0)
That works fine.
I tilt the circle with an angle to the horizontal layer. I call this angleXY.
The circle cuts through the horizontal layer in the X-axis. The circle is tiltet counter-clockwise. This also works fine.
But the problem occures when I try to rotate the tilted circle counterclockwise around the z-axis. The angle is vinkeXZ. I can't figure out how to calculate the x-coordinates.

Here is the code (vinkel = angle)
fromDegrees = 10
toDegrees = 360
stepDegrees = 10
centerX = 0
centerY = 0
centerZ = 0
radiusP = 0.5
vinkelXZ = 45 ! Angle from the X-axis counterclockwise around the Z-axis (centerX and centerY=0)
vinkelXY = 45 ! Angle between the horizontal-layer and the circle.
! Counterclockwise around the X-axis (centerY=0)
angle = 0
GOSUB "GenerateCircularCoordinates"


END


"GenerateCircularCoordinates":
! This routine calculates xyz-coordinates to a circle that tilts against the horizontal-layer
! and rotates around the Z-axis
!
! Calculate the trigonometric factores to angles that do not change in the loop.
sinVinkelXY = SIN(vinkelXY)
cosVinkelXY = COS(vinkelXY)
sinVinkelXZ = SIN(vinkelXZ)
cosVinkelXZ = COS(vinkelXZ)

FOR vinkel = fromDegrees TO toDegrees STEP stepDegrees
deltaX = radiusP * COS (vinkel)
deltaY = radiusP * SIN (vinkel)
deltaZ = radiusP * SIN (vinkel)

x = centerX - deltaX
y = centerY - deltaY
z = centerZ
! ---------------------------------------------------
! Tilt against the horizontal-layer (XY-layer)
! Rotation around the X-axis
!
z = -y * sinVinkelXY + centerZ
y = y * cosVinkelXY + centerY
! ---------------------------------------------------
! Rotation around the Z-axis
!
y = y + x*sinVinkelXZ
x = x*cosVinkelXZ
!
! PUT x, y, z, angle
IF vinkel <> 0 THEN
ADD x, y, z
TEXT 0.005, 0, vinkel
DEL 1
LIN_ x - 0.01, y - 0.01, z - 0.01, x + 0.01, y + 0.01, z + 0.01
!ENDIF

NEXT vinkel
RETURN

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