Ray 3D

Enter the parametric equation of the surface here:
Note that the surface must be defined and continuous for all $u$ , $v$ in or near the range (minimum distance less than $\frac{0.0001}{a_{cnt}} (a_{\max} - a_{\min})$ , where $a$ is $u$ $v$ ), and must be smooth for all $u$ and $v$ in the range. Singular points will be plotted inaccurately, sometimes the calculation even fails.
- $x (u, v) =$
- $y (u, v) =$
- $z (u, v) =$
Enter the range for $u$ and $v$ :
- $u_{\min} =$ , $u_{\max} =$
- $v_{\min} =$ , $v_{\max} =$
In order to draw the image, we must subdivide $[u_{\min}, u_{\max}]$ and $[v_{\min}, v_{\max}]$ into $u_{cnt}$ and $v_{cnt}$ equal subdivisions, and calculate the coordinates and normals (for smoothening) of the resulting $u_{cnt} \times v_{cnt}$ lattice points. Of course, the larger $u_{cnt}$ and $v_{cnt}$ is, the more accurate the resulting surface is. Generally 12x12 is already quite satisfactory, and can usually be calculated in several seconds. However, if you need high quality, 24x24 should be OK, but you will need to wait for 10 or more seconds. Note that transforming the equations to a good form is vital to the quality of the image.
Enter $u_{cnt}$ and $v_{cnt}$ here:
- $u_{cnt} =$ ,
- $v_{cnt} =$
Enter the ranges for $x$ , $y$ , and $z$ :
Portions of the surface outside of this range is clipped. This is useful for examing the interior of the image. However, if you want to see the full image, specify a wide range that will fit in all the points on the surface. Note that this does not affect your camera view, thus a moderately large range and a extremely large range acts exactly the same for finite surfaces.
- $x_{\min} =$ , $x_{\max} =$
- $y_{\min} =$ , $y_{\max} =$
- $z_{\min} =$ , $z_{\max}$ =
Enter the ranges for $x$ , $y$ , and $z$ :
Portions of the surface outside of this range is clipped. This is useful for examing the interior of the image. However, if you want to see the full image, specify a wide range that will fit in all the points on the surface. Note that this does not affect your camera view, thus a moderately large range and a extremely large range acts exactly the same for finite surfaces.
- Camera: $x =$ , $'' is not valid.
  
  If you see this message, it is usually due to a bug in the module
  `tool/geometry/ray3d.en'.
  
  Please contact the module's developer about the bug.$