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If the four points are:
Then this is a valid system of basis.
MS Quick Basic -program to calculate if the system is valid for transformation.
DIM L(4), x(4), y(4), z(4)
L(1) = 0
L(2) = 0
L(3) = 0
L(4) = 0
x(1) = 0
x(2) = .5
x(3) = .5
x(4) = 1
y(1) = 0
y(2) = .288675
y(3) = .866025
y(4) = 0
z(1) = 0
z(2) = .866025
z(3) = 0
z(4) = 0
xxx = (GAMMAxz(1, 4, 3, 2, x(), z()) * GAMMAyz(4, 3, 2, 1,
y(), z()) - GAMMAxz(4, 3, 2, 1, x(), z()) * GAMMAyz(1, 4, 3, 2, y(), z()))
yyy = (GAMMAyz(1, 4, 3, 2, y(), z()) * GAMMAxz(4, 3, 2, 1,
x(), z()) - GAMMAyz(4, 3, 2, 1, y(), z()) * GAMMAxz(1, 4, 3, 2, x(), z()))
zzz = (GAMMAxz(3, 2, 4, 1, x(), z()) * GAMMAxy(2, 1, 3, 4,
x(), y()) - GAMMAxz(2, 1, 3, 4, x(), z()) * GAMMAxy(3, 2, 4, 1, x(), y()))
CLS
PRINT xxx
PRINT yyy
PRINT zzz
FUNCTION BETAx (a, b, x())
BETAx = 2 * (x(b) - x(a))
END FUNCTION
FUNCTION BETAy (a, b, y())
BETAy = 2 * (y(b) - y(a))
END FUNCTION
FUNCTION BETAz (a, b, z())
BETAz = 2 * (z(b) - z(a))
END FUNCTION
FUNCTION GAMMAxy (a, b, c, d, x(), y())
GAMMAxy = BETAx(a, b, x()) * BETAy(c, d, y()) - BETAx(d, c,
x()) * BETAy(b, a, y())
END FUNCTION
FUNCTION GAMMAxz (a, b, c, d, x(), z())
GAMMAxz = BETAx(a, b, x()) * BETAz(c, d, z()) - BETAx(d, c,
x()) * BETAz(b, a, z())
END FUNCTION
FUNCTION GAMMAyz (a, b, c, d, y(), z())
GAMMAyz = BETAy(a, b, y()) * BETAz(c, d, z()) - BETAy(d, c,
y()) * BETAz(b, a, z())
END FUNCTION
FUNCTION sqr2 (a)
sqr2 = a * a
END FUNCTION
Requires Windows 95 or higher .
Click to
Download.Ibrahim M. Hijazi
April ,2003