s for sin
c for cos
l is length (in this case radio)
These are the equations.
Torus coil.
/* For cartesian coordinate system, enter parametric equation
/* in terms of t (which will vary from 0 to 1) for x, y and z
/* For example: for a circle in x-y plane, centered at origin
/* and radius = 4, the parametric equations will be:
/* x = 4 * cos ( t * 360 )
/* y = 4 * sin ( t * 360 )
/* z = 0
/*-------------------------------------------------------------------
/*coils
n=10
/*torus radio
l1 = 25
/*coil radio
l2 = 5
/*torus total angle
omega1 = 360
/*coils total angle
omega2 = n * omega1
/* torus actual angle
teta1 = omega1*t
/*coils actual angle
teta2 = omega2*t
/* trigonometric simplifications
c1 = cos(teta1)
s1 = sin(teta1)
c2 = cos(teta2)
s2 = sin(teta2)
/* cartesian parameters
x = c1*(l1 + l2*c2)
y = s1*(l1 + l2*c2)
z = l2*s2
Helical coil.
/* For cartesian coordinate system, enter parametric equation
/* in terms of t (which will vary from 0 to 1) for x, y and z
/* For example: for a circle in x-y plane, centered at origin
/* and radius = 4, the parametric equations will be:
/* x = 4 * cos ( t * 360 )
/* y = 4 * sin ( t * 360 )
/* z = 0
/*-------------------------------------------------------------------
/*number of torus
n1 = 2
/*coils per torus
n2 = 40
/*torus radio
l1 = 10
/*coil radio
l2 = 2
/*torus total angle
omega1 = n1 * 360
/*coils total angle
omega2 = n2 * omega1
/* torus actual angle
teta1 = omega1*t
/*coils actual angle
teta2 = omega2*t
/* trigonometric simplifications
c1 = cos(teta1)
s1 = sin(teta1)
c2 = cos(teta2)
s2 = sin(teta2)
/* cartesian parameters
x = c1*(l1 + l2*c2)
y = s1*(l1 + l2*c2)
/* z = l2*s2
/* every torus turn z value afected by 3 coil radus
z = (l2*s2)+3*n1*l2*t
Coiled helical halo.
/* For cartesian coordinate system, enter parametric equation
/* in terms of t (which will vary from 0 to 1) for x, y and z
/* For example: for a circle in x-y plane, centered at origin
/* and radius = 4, the parametric equations will be:
/* x = 4 * cos ( t * 360 )
/* y = 4 * sin ( t * 360 )
/* z = 0
/*-------------------------------------------------------------------
/*helix waves in halo
n2 = 10
/*coils per helix
n3 = 10
/*halo radio
l1 = 36
/*helix radio
l2 = 6
/*coil radio
l3 = 1
/*halo total angle or speed
omega1 = 360
/*helix total angle or speed
omega2 = n2 * omega1
/*coil total angle or speed
omega3 = n3 * omega2
/* halo actual angle
teta1 = omega1*t
/*helix actual angle
teta2 = omega2*t
/*coil actual angle
teta3 = omega3*t
/* trigonometric simplifications
c1 = cos(teta1)
s1 = sin(teta1)
c2 = cos(teta2)
s2 = sin(teta2)
c3 = cos(teta3)
s3 = sin(teta3)
/* cartesian parameters
X = c1*(c2*(c3*l3+l2)+l1)-l3*s1*s3
y = c1*l3*s3+(c2*(c3*l3+l2)+l1)*s1
z = (c3*l3+l2)*s2
Those are the matrix of homogeneus transformation.
/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 11.04.0 ] */
/* [wxMaxima: input start ] */
rotz1: matrix(
[c1,-s1,0,0],
[s1,c1,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
trasx1: matrix(
[1,0,0,l1],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotx1: matrix(
[1,0,0,0],
[0,0,-1,0],
[0,1,0,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotz2: matrix(
[c2,-s2,0,0],
[s2,c2,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
trasx2: matrix(
[1,0,0,l2],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotx2: matrix(
[1,0,0,0],
[0,0,1,0],
[0,-1,0,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
p2: matrix(
[0],
[0],
[0],
[1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotz1.trasx1.rotx1.rotz2.trasx2.rotx2.p2;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotz3: matrix(
[c3,-s3,0,0],
[s3,c3,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
trasx3: matrix(
[1,0,0,l3],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotx3: matrix(
[1,0,0,0],
[0,0,-1,0],
[0,1,0,0],
[0,0,0,1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
p3: matrix(
[0],
[0],
[0],
[1]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
rotz1.trasx1.rotx1.rotz2.trasx2.rotx2.rotz3.trasx3.rotx3.p3;
/* [wxMaxima: input end ] */
/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$
best regards.
