BEGINCAD
DIMENSION
3
INPUTVARIABLES
(X,Y,Z)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
Z**2 + Y**2 + X**2 - 1 $
)
BASIS
(
Z**2 + Y**2 + X**2 - 1 $
)
CONTENTS
(
)
PROJECTION
(
1 $ ,
4 Y**2 + 4 X**2 - 4 $
)

CELLS

BEGINCELL
INDEX
(1,1,1)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 3 )
(0)
(0)
)
DEFININGFORMULA
( ( ( X + 1 < 0 ) & ( 0= 0 ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,1,1)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( ( X + 1 = 0 ) & ( Y < 0 ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,2,1)
INPUTSIGNATURE
(EQ)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( ( X + 1 = 0 ) & ( Y = 0 ) ) & ( Z < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,2,2)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(0)
(0)
)
DEFININGFORMULA
( ( ( X + 1 = 0 ) & ( Y = 0 ) ) & ( Z = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(0)
( 2 )
)
DEFININGFORMULA
( ( ( X + 1 = 0 ) & ( Y = 0 ) ) & ( Z > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
( 2 )
(0)
)
DEFININGFORMULA
( ( ( X + 1 = 0 ) & ( Y > 0 ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 > 0
) ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
(- 1 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
(0)
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
( 2 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 <
0 ) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( Z < 0
) & ( Z**2 + Y**2 + X**2 - 1 > 0 ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(-1 , -3/4)
POINT
(
(- 1/2 )
(0)
( U )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 <
0 ) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( Z < 0
) & ( Z**2 + Y**2 + X**2 - 1 = 0 ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(0)
(0)
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 <
0 ) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( ( Z <
0 ) & ( Z**2 + Y**2 + X**2 - 1 < 0 ) ) | ( Z = 0 ) | ( ( Z > 0 ) & ( Z**2 +
Y**2 + X**2 - 1 < 0 ) ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(0 , 1)
POINT
(
(- 1/2 )
(0)
( U )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 <
0 ) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( Z > 0
) & ( Z**2 + Y**2 + X**2 - 1 = 0 ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(0)
( 3 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 <
0 ) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( Z > 0
) & ( Z**2 + Y**2 + X**2 - 1 > 0 ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(0 , 1)
POINT
(
(- 1/2 )
( U )
(- 1 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(0 , 1)
POINT
(
(- 1/2 )
( U )
(0)
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(0 , 1)
POINT
(
(- 1/2 )
( U )
( 2 )
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 = 0
) ) ) & ( Z > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
( 3 )
(0)
)
DEFININGFORMULA
( ( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 > 0
) ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( ( X - 1 = 0 ) & ( Y < 0 ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( ( X - 1 = 0 ) & ( Y = 0 ) ) & ( Z < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(0)
(0)
)
DEFININGFORMULA
( ( ( X - 1 = 0 ) & ( Y = 0 ) ) & ( Z = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(0)
( 2 )
)
DEFININGFORMULA
( ( ( X - 1 = 0 ) & ( Y = 0 ) ) & ( Z > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
( 2 )
(0)
)
DEFININGFORMULA
( ( ( X - 1 = 0 ) & ( Y > 0 ) ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(5,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
( 3 )
(0)
(0)
)
DEFININGFORMULA
( ( ( X - 1 > 0 ) & ( 0= 0 ) ) & ( 0= 0 ) ) $
ENDCELL


INDUCEDCAD
BEGINCAD
DIMENSION
2
INPUTVARIABLES
(X,Y)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
1 $ ,
4 Y**2 + 4 X**2 - 4 $
)
BASIS
(
Y**2 + X**2 - 1 $
)
CONTENTS
(
)
PROJECTION
(
1 $ ,
- 4 X**2 + 4 $
)

CELLS

BEGINCELL
INDEX
(1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 3 )
(0)
)
DEFININGFORMULA
( ( X + 1 < 0 ) & ( 0= 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(- 1 )
)
DEFININGFORMULA
( ( X + 1 = 0 ) & ( Y < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
(0)
)
DEFININGFORMULA
( ( X + 1 = 0 ) & ( Y = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
( 2 )
)
DEFININGFORMULA
( ( X + 1 = 0 ) & ( Y > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(- 1 )
)
DEFININGFORMULA
( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 > 0 )
) ) $
ENDCELL

BEGINCELL
INDEX
(3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
)
DEFININGFORMULA
( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y < 0 ) & ( Y**2 + X**2 - 1 = 0 )
) ) $
ENDCELL

BEGINCELL
INDEX
(3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
(0)
)
DEFININGFORMULA
( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( ( Y < 0 ) & ( Y**2 + X**2 - 1 < 0
) ) | ( Y = 0 ) | ( ( Y > 0 ) & ( Y**2 + X**2 - 1 < 0 ) ) ) ) $
ENDCELL

BEGINCELL
INDEX
(3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
4 U**2 - 3 $ ,
(0 , 1)
POINT
(
(- 1/2 )
( U )
)
DEFININGFORMULA
( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 = 0 )
) ) $
ENDCELL

BEGINCELL
INDEX
(3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
( 3 )
)
DEFININGFORMULA
( ( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) & ( ( Y > 0 ) & ( Y**2 + X**2 - 1 > 0 )
) ) $
ENDCELL

BEGINCELL
INDEX
(4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(- 1 )
)
DEFININGFORMULA
( ( X - 1 = 0 ) & ( Y < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
(0)
)
DEFININGFORMULA
( ( X - 1 = 0 ) & ( Y = 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
( 2 )
)
DEFININGFORMULA
( ( X - 1 = 0 ) & ( Y > 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
( 3 )
(0)
)
DEFININGFORMULA
( ( X - 1 > 0 ) & ( 0= 0 ) ) $
ENDCELL


INDUCEDCAD
BEGINCAD
DIMENSION
1
INPUTVARIABLES
(X)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
1 $ ,
- 4 X**2 + 4 $
)
BASIS
(
X + 1 $ ,
X - 1 $
)
CONTENTS
(
)
PROJECTION
(
)

CELLS

BEGINCELL
INDEX
(1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 3 )
)
DEFININGFORMULA
( X + 1 < 0 ) $
ENDCELL

BEGINCELL
INDEX
(2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U + 1 $ ,
(-2 , -1)
POINT
(
(- 1 )
)
DEFININGFORMULA
( X + 1 = 0 ) $
ENDCELL

BEGINCELL
INDEX
(3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
(- 1/2 )
)
DEFININGFORMULA
( ( X + 1 > 0 ) & ( X - 1 < 0 ) ) $
ENDCELL

BEGINCELL
INDEX
(4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U - 1 $ ,
(0 , 2)
POINT
(
( 1 )
)
DEFININGFORMULA
( X - 1 = 0 ) $
ENDCELL

BEGINCELL
INDEX
(5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
U $ ,
(0 , 0)
POINT
(
( 3 )
)
DEFININGFORMULA
( X - 1 > 0 ) $
ENDCELL


ENDCAD
ENDCAD
ENDCAD