Volume representing an (almost)arbitrary 8 vertices solid.
The solid is defined by two quadrilaterals sitting on parallel planes,
the distance between these two planes is dz*2.
The base quadrilateral contained within the plane located at -dz is defined by
the first 4 vertices (v1,v2,v3,v4 each one with the x and y coordinates).
The other parallel quadrilateral contained within the plane at +dz is defined by
the other 4 vertices (v5,v6,v7,v8 each one with the x and y coordinates).
CSG cone or cone segment described by
rmin1 inside radius at z/2
rmin2 inside radius at z/2
rmax1 outside radius at z/2
rmax2 outside radius at z/2
z length in z
startphi starting angle of the segment in radians
deltaphi delta angle of the segment in radians
CSG cut tube or cut tube segment solid described by
rmin Inner radius
rmax Outer radius
z length in z
startphi The starting phi angle in radians, adjusted such that (startphi+deltaphi <= 2PI, startphi > -2PI)
deltaphi Delta angle of the segment in radians
lowX, lowY, lowZ Normal at lower Z plane
highX, highY, highZ Normal at higher Z plane
CSG ellispoid or ellipsoidal shell segment solid described by
ax x semiaxis
by y semiaxis
cz z semiaxis
zcut1 bottom plane cutting ellipsoid
zcut2 top plane cutting ellispoid
CSG parallelepiped solid is described by
x, y, z length in x,y,z
alpha Angle formed by the y axis and by the plane joining the centre of the faces
G4Parallel to the z-x plane at -y and +y
theta Polar angle of the line joining the centres of the faces at -z and +z in z
phi Azimuthal angle of the line joining the centres of the faces at -z and +z in z
CSG polycone or polycone segment described by
startphi starting angle of the segment in radians
deltaphi delta angle of the segment in radians
and a set of z-planes each described by
rmin inside radius at z/2
rmax outside radius at z/2
z length in z
Reflected solid:
sx, sy, sz are scale components (containing reflection),
rx, ry, rz are rotation angles around given axes and
dx, dy, dz is the translation.
CSG sphere or spherical shell segment solid described by
rmin inner radius
rmax outer radius
startphi starting angle of the segment in radians(0 <= phi <= 2*PI)
deltaphi delta angle of the segment in radians
starttheta starting angle of the segment in radians(0 <= theta <= PI)
deltatheta delta angle of the segment in radians
CSG torus solid is described by
rmin Inside radius
rmax Outside radius
rtor swept radius of torus
startphi The starting phi angle in radians adjusted such that sphi+dphi lt 2PI, sphi gt -2PI
deltaphi Delta angle of the segment in radians
CSG general trapezoid solid is described by
z Length along the z-axis
theta Polar angle of the line joining the centres of the faces at -/+z
phi Azimuthal angle of the line joing the centre of the face at -z to the centre of the face at +z
y1 Length along y of the face at -z
x1 Length along x of the side at y = -y1 of the face at -z
x2 Length along x of the side at y = +y1 of the face at -z
alp1 Angle with respect to the y axis from the centre of the side at y =- y1 to the centre at y = +y1 of the face at -z
y2 Length along y of the face at +z
x3 Length along x of the side at y = -y2 of the face at +z
x4 Length along x of the side at y = +y2 of the face at +z
alp2 Angle with respect to the y axis from the centre of the side at y = -y2 to the centre at y = +y2 of the face at +z
CSG trapezoid solid with varying x and y dimensions along z axis
x1 Length along x at the surface positioned at -z
x2 Length along x at the surface positioned at +z
y1 Length along y at the surface positioned at -z
y2 Length along y at the surface positioned at +z
z Length along z axis
CSG tube or tube segement solid described by
rmin Inner radius
rmax Outer radius
z length in z
startphi The starting phi angle in radians, adjusted such that
(startphi+deltaphi <= 2PI, startphi > -2PI)
deltaphi Delta angle of the segment in radians
general twisted trapezoid. faces perpendicular to the z planes are trapezia, and their centres are
not necessarily on a line paralell to the z axis.
PhiTwist Twist Angle
z length along the z-axis
Theta Polar angle of the line joining the centres of the faces at -/+z
Phi Azimuthal angle of the line joing the centre of the face at -z to the centre of the face at +z
y1 length along y of the face at -z
x1 length along x of the side at y=-y1 of the face at -z
x2 length along x of the side at y=+y1 of the face at -z
y2 length along y of the face at +z
x3 length along x of the side at y=-y2 of the face at +z
x4 length along x of the side at y=+y2 of the face at +z
Alph Angle with respect to the y axis from the centre of the side
different length axis twistable trapezoid. faces perpendicular to the z planes are trapezia, and their centres are
not necessarily on a line paralell to the z axis.
PhiTwist Twist Angle
z length along the z-axis
y1 length along y of the face at -z
x1 length along x of the side at y=-y1 of the face at -z
x2 length along x of the side at y=+y1 of the face at -z
y2 length along y of the face at +z
CSG twisted tube segement solid described by
twistedangle twist angle
endinnerrad inside radius at end of segment
endouterrad outside radius at end of segment
zlen z length of segment
phi phi angle of a segment
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