Design of an algorithm for Shading and Blocking:
Inputs:
Mirror length – HL
Mirror width - HW
Mirror Position (Xm, Ym)
Azimuthal - Ө
Altitude- Ø
Sun’s vector (Xs, Ys, Zs)
Mirror Normal (Xn, Yn, Zn)
Algorithm:
1. For each mirror print Xm,Ym values
2. Print central mirror position Xm,Ym,Zm (Assuming Zm=0)
3. Print central mirror normal Xn,Yn,Zn
4. Calculate mirror co-ordinates in Heliostat co-ordinate system
A (-HL/2,-HW/2, 0)
B (+HL/2,-HW/2, 0)
C (+HL/2, +HW/2, 0)
D (-HL/2, +HW/2, 0)
5. Calculate Central Mirror in absolute co-ordinate system:
For each point A, B, C, D, We need 2 rotations and 1 translation; For (X, Y, Z)
Ø rotation: (Elevation i.e. Altitude)
Ө rotation: (Azimuthal)
Translation:
(XF, YF, ZF) are values driven with respect to each point A,B,C or D in absolute co-
ordinate system.
6. Compute mirror co-ordinates in absolute co-ordinate system
A: XA YA ZA
B: XB YB ZB
C: XC YC ZC
D: XD YD ZD
7. Compute neighboring mirror absolute co-ordinates:
ΔR= 2*Diagonal
ΔA=1.5*Diagonal
Diagonal=√H²+W²
Mirror-1 Co-ordinates:
A: (XA+ ΔA, YA, ZA)
B: (XB+ ΔA, YB, ZB)
C: (Xc+ ΔA, Yc, Zc)
D: (XD+ ΔA, YD, ZD)
Mirror-2 Co-ordinates:
A: (XA- ΔA, YA, ZA)
B: (XB- ΔA, YB, ZB)
C: (XC- ΔA, Yc, Zc)
D: (XD- ΔA, YD, ZD)
Mirror-3 Co-ordinates:
A: (XA+1/2 ΔA, YA -ΔR, ZA)
B: (XB+1/2 ΔA, YB-ΔR, ZB)
C: (Xc+1/2 ΔA, Yc-ΔR, Zc)
D: (XD+1/2ΔA, YD-ΔR, ZD)
Mirror-4 Co-ordinates:
A: (XA-1/2 ΔA, YA -ΔR, ZA)
B: (XB-1/2 ΔA, YB-ΔR, ZB)
C: (Xc-1/2 ΔA, Yc-ΔR, Zc)
D: (XD-1/2ΔA, YD-ΔR, ZD)
Mirror-5 Co-ordinates:
A: (XA+1/2 ΔA, YA +ΔR, ZA)
B: (XB+1/2 ΔA, YB+ΔR, ZB)
C: (Xc+1/2 ΔA, Yc+ΔR, Zc)
D: (XD+1/2ΔA, YD+ΔR, ZD)
Mirror-6 Co-ordinates:
A: (XA-1/2 ΔA, YA +ΔR, ZA)
B: (XB-1/2 ΔA, YB+ΔR, ZB)
C: (Xc-1/2 ΔA, Yc+ΔR, Zc)
D: (XD-1/2ΔA, YD+ΔR, ZD)
Mirror-7 Co-ordinates:
A: (XA, YA -2ΔR, ZA)
B: (XB, YB-2ΔR, ZB)
C: (XC, Yc-2ΔR, Zc)
D: (XD, YD-2ΔR, ZD)
Mirror-8 Co-ordinates:
A: (XA, YA +2ΔR, ZA)
B: (XB, YB+2ΔR, ZB)
C: (XC, Yc+2ΔR, Zc)
D: (XD, YD+2ΔR, ZD)
8. For each mirror, find the projections of mirror on to the center mirror plane. This
can be done using the rayPlane utility offered by Java3D.
9. Find the intersection area of the central mirror and the projected plane, which is
nothing but shading/blocking using the Clip function.