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Math Library

   

Some basic examples with curves and surfaces that demonstrate how to use the Math-Plugin. There will be more parametric objects to download later.

 

 

Sine Graph

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
2 * PI
13
t
sin ( t )
0


 

Circle

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
2 * PI
25
cos ( t ) * Radius
sin ( t ) * Radius
0
Radius = 1


 

Helix

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
6 * PI
25
cos ( t )
sin ( t )
t / 8


 

Progressiv Helix

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
8 * PI
25
cos ( t )
sin ( t )
t^2 / 200


 

Quinta Interference

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
4 * PI
55
t
( sin ( 2*t ) + sin ( 3*t) ) *scale
0
scale = 3


 

Involute of Circle

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0.1
4 * PI
101
2 * (cos(t) + t * sin(t))
2 * (sin(t) - t * cos(t))
0


 

Spherical Spiral

Minimum t
Maximum t
PointCount
Function X(t)
Function Y(t)
Function Z(t)
Variables

0
PI
29
cos( Turns *2*t) * sin(t)
sin( Turns *2*t) * sin(t)
cos(t)
Turns =5


 

Wave

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2 * PI
0
2 * PI
13
13
u
v
cos(U) + sin(v)


 

Sphere

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

-PI/2
3/2*PI
-PI/2
PI/2
13
13
cos(v)*cos(u) * Radius
cos(v)*sin(u) * Radius
sin(v) * Radius
Radius = 1


 

Torus

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2*PI
0
2*PI
25
25
cos(u)*(tr*cos(v)+ir)
sin(u)*(tr*cos(v)+ir)
tr*sin(v)
tr=2 , ir=4


 

Cylinider

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2*PI
0
2*PI
17
4
cos(u) * Radius
sin(u) * Radius
v / ( 2*PI ) * Height
Radius = 2 , Height = 5


 

Moebius Strip

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2*PI
-1
1
17
4
sin(u)*(-2+v*sin(u/2))
cos(u)*(-2+v*sin(u/2))
v*cos(u/2)


 

Moebius Strip Closed

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
4*PI
-1
1
35
4
sin(u)*(-2+v*sin(u/2))
cos(u)*(-2+v*sin(u/2))
v*cos(u/2)


 

Stereographic Sphere

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

-3
3
-3
3
25
25
2*u/(u*u+v*v+1)
2*v/(u*u+v*v+1)
(u*u+v*v-1)/(u*u+v*v+1)


 

Catalan

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

-PI
3*PI
-2
2
35
13
sin(PI/2)*(-HCos(v)*sin(u)+u-pi)+cos(PI/2)*(-HSin(v)*cos(u)+v)
sin(PI/2)*(-HCos(v)*cos(u))+cos(PI/2)*(HSin(v)*sin(u))
sin(PI/2)*(-HSin(v/2)*sin(u/2)*4)+cos(PI/2)*(-HCos(v/2)*cos(u/2)*4+4)


 

Elliptic Paraboloid

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2*PI
0
3
25
13
v * cos(u) * Xscale
v * sin(u) * Yscale
v^2
Xscale = 2 , Yscale = 3


 

Catenoid Helicoid

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

-PI
PI
-2
2
25
13
cos(a)*cos(u)*HCos(v)+sin(a)*sin(u)*HSin(v)
-cos(a)*sin(u)*HCos(v)+sin(a)*cos(u)*HSin(v)
cos(a)*v+sin(a)*u
a=PI/2


 

Klein Surface

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
2*PI
0
2*PI
25
25
(1 + cos(u/2)*sin(v) - sin(u/2)*sin(2*v))*cos(u)
(1 + cos(u/2)*sin(v) - sin(u/2)*sin(2*v))*sin(u)
sin(u/2)*sin(v) + cos(u/2)*sin(2*v)


 

Enneper 2

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
1
-PI
PI
7
25
u*cos(v)-u^(2* Sym -1)/(2* Sym -1)*cos((2* Sym -1)*v)
-u*sin(v)-u^(2* Sym -1)/(2* Sym -1)*sin((2* Sym -1)*v)
2/ Sym *u^ Sym *cos( Sym *v)
Sym=2


 

Enneper 3

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
1
-PI
PI
7
25
u*cos(v)-u^(2* Sym -1)/(2* Sym -1)*cos((2* Sym -1)*v)
-u*sin(v)-u^(2* Sym -1)/(2* Sym -1)*sin((2* Sym -1)*v)
2/ Sym *u^ Sym *cos( Sym *v)
Sym=3


 

Enneper 4

Minimum u
Maximum u
Minimum v
Maximum v
PointCount u
PointCount v
Function X(u,v)
Function Y(u,v)
Function Z(u,v)
Variables

0
1.2
-PI
PI
7
25
u*cos(v)-u^(2* Sym -1)/(2* Sym -1)*cos((2* Sym -1)*v)
-u*sin(v)-u^(2* Sym -1)/(2* Sym -1)*sin((2* Sym -1)*v)
2/ Sym *u^ Sym *cos( Sym *v)
Sym=4

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