Surface by formula

 

 

 

Links/Videos:

 

 

This command allows to create a surface with 3 formulas

 

Creation stages / Use:

 

Click the icon or select the Surface > Surface by formula... command from the drop-down menu.

 

  1. Enter formulas for X(u,v), Y(u,v) and Z(u,v).

  2. Enter Minimum and Maximum intervals of u and v.

  3. Check if intervals are Periodics.

  4. Reverse intervals if needed

  5. Select the positioning frame of the surface.

  6. Enter the modeling tolerance.

  7. Validate by clicking .

 

 

It is important to systematically specify the unit of entered values in expressions. Otherwise, u and v parameters have no unit.

 

 

Available Options:

 

 

 

If the edge following u or y has to be closed, you have to check periodic. For example, a torus (see below) the section (u) is closed therefore periodic , the trajectory is cylindric (also closed, therefore periodic).

 

 

 

u and v are inside the interval [minimum value, maximum value]. By clicking the Reverse option, the interval taken into account is [maximum value, minimum value]. It is equivalent to replace u by u max - u + u min.

 

 

 

This option allows to modify the modeling tolerance. By default this modeling tolerance is set in the document options.

 

 

The more the tolerance is precise, the more the geometry will be precise. The default value is a good compromise between geometry accuracy and performance.

 

 

  • A finer tolerance (for example 0.01 instead of 0.1) needs more important calculation time.

  • If the modeling tolerance is modified in the document options, manually modified tolerances with this command will not change.

 

 

 

 

 

To measure the surface quality, TopSolid calculates the distance between points on the created Bspline surface and those calculated by the formula.

If the tolerance is not reached for some points of the Bspline surface, TopSolid inserts parameters where the accuracy is not reached and calculates again the surface. TopSolid iterates several times to locally refine the surface and reach the accuracy. To guarantee a better surface quality, TopSolid measures several points per tile (a tile corresponds to u which varies between [ui ; ui+1] and v which varies between [vj ; vj+1]), so 9 points are positioned at ¼, ½ and ¾ of intervals

The quality measures uses a lot of system resources. If the "Simplify" option is not checked, the precise mode is activated (measure of 9 points per tile). If it is checked, the approximative mode is activated (measure of 1 point per tile).

 

 

For below examples, the result is the same with or without the option checked (except for the "eggs box"), but the calculating time is faster with the option checked.

 

 

 

Examples:

 

 

Formulas:

Values signification:

Result:

  • X(u,v)

(30mm+5mm*cos(u*360°))*cos(v*360°)

  • Y(u,v)

(30mm+5mm*cos(u*360°))*sin(v*360°)

  • Z(u,v)

5mm*sin(u*360°)

  • u and v intervals

u and v are periodics, their minimum value is 0, their maximum is 1 (without unit)

 

 

Formulas:

Values signification:

Result:

  • X(u,v)

1mm*u*cos(v*360°)

  • Y(u,v)

1mm*u*sin(v*360°)

  • Z(u,v)

5mm*v (5mm is the pitch)

  • u and v intervals

u and v aren't periodics, u changes from 0 to 2 (which is the helicoid radius), v changes from 0 to 5 which is the number of turns.

4 is the diameter (the entered radius is 2)

5 is the pitch

 

 

Formulas:

Values signification:

Result:

  • X(u,v)

3mm*sqrt(1+u*u)*cos(v*360°)

  • Y(u,v)

3mm*sqrt(1+u*u)*sin(v*360°)

  • Z(u,v)

5mm*u (5mm is the base height)

  • u and v intervals

v is periodic, u changes from 0 to 3 (which is the helicoid radius), v changes from 0 to 1 which is the number of turns.

6 is the diameter (the entered radius is 3 for X and for Y)

15 is the height (see Z)

 

 

Formulas:

Values signification:

Result:

  • X(u,v)

50mm*cos(v*360°)*cos(u*360°)+u*1mm

  • Y(u,v)

50mm*sin(v*360°)*cos(u*360°)+u*1mm

  • Z(u,v)

10mm*sin(u*360°)

  • u and v intervals

u changes from 0 to 0.25, v from 0 to 1.

 

50mm is the radius ( X and Y)

10mm is the height (following Z)

 

 

Formulas:

Values signification:

Result:

  • X(u,v)

50mm*u

  • Y(u,v)

20mm*v

  • Z(u,v)

20mm*(u*u-v*v)  

  • u and v intervals

u and v change from -1 to 1.

 

50mm is the biggest radius

20mm is the smallest radius

 

 

Formulas:

Result:

  • X(u,v)

u*cos(v*360°)*50mm

  • Y(u,v)

50mm*tan(v*360°)

  • Z(u,v)

50mm*u*sin(v*360°)  

  • u and v intervals

u changes from -1 to 1, v from -0.1 to 0.1

 

 

Formulas:

Result:

  • X(u,v)

50mm*cos(u*360°)*cos(v*360°)

  • Y(u,v)

50mm*sin(u*360°)*cos(v*360°)

  • Z(u,v)

50mm*sin(v*360°)  

  • u and v intervals

u changes from 0 to 0.5, v from -0.1 to 0.1

 

50mm is the sphere radius

 

 

Formulas:

Result with intervals [-1 ; 1] :

Result with intervals [-5 ; 5] :

  • X(u,v)

1mm*u

  • Y(u,v)

1mm*v

  • Z(u,v)

0,5mm*cos(u*360°)*sin(v*360°)

  • u and v intervals

u and v change from -1 to 1, then from -5 to 5.

 

 

 

 

Formulas:

Result:

  • X(u,v)

10mm*u

  • Y(u,v)

10mm*sin(v*90°)*(1+cos(u*360°)/5)

  • Z(u,v)

10mm*cos(v*90°)*(1+cos(u*360°)/5)

  • u and v intervals

v is periodic, u changes from -5 to 5 (the number of pitches is centered with the frame ), v changes from -2 to 2 (4 x 1/4 of turn).

 

 

 

Formulas with parameters:

Result:

  • X(u,v)

F*sin((P*u+v)*1°)

  • Y(u,v)

(G-F*cos((P*u+v)*1°))*cos(u*1°)

  • Z(u,v)

(G-F*cos((P*u+v)*1°))*sin(u*1°)

  • Intervals u

Minimum : -1620

Maximum : 1260

  • Intervals v

Minimum : 0.6

Maximum : 6.6

 

 

 

Modifications:

 

The surface can be modified with the Edit.. contextual command from the surface of from the operations tree.

 

Additional information: