Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:05:05Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:27:03Z

1 revision: Initial Load (TF)

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[[Category:Objects]]
[[Category:Finite Patch Primitives]]
{{#indexentry:bezier}}
{{#indexentry:bezier patch}}
{{#indexentry:bicubic_patch, keyword}}
{{#indexentry:keyword, bicubic_patch}}
A <code>bicubic_patch</code> is a 3D curved surface created from a mesh of
triangles. POV-Ray supports a type of bicubic patch called a Bezier
patch. A bicubic patch is defined as follows:
<pre>
BICUBIC_PATCH:
bicubic_patch {
PATCH_ITEMS...
<Point_1>,<Point_2>,<Point_3>,<Point_4>,
<Point_5>,<Point_6>,<Point_7>,<Point_8>,
<Point_9>,<Point_10>,<Point_11>,<Point_12>,
<Point_13>,<Point_14>,<Point_15>,<Point_16>
[OBJECT_MODIFIERS...]
}
PATCH_ITEMS:
type Patch_Type | u_steps Num_U_Steps | v_steps Num_V_Steps |
flatness Flatness
</pre>

{{#indexentry:default values, bicubic_patch}}
Bicubic patch default values:
<pre>
flatness : 0.0
u_steps : 0
v_steps : 0
</pre>

{{#indexentry:type, bicubic_patch}}
{{#indexentry:keyword, type}}
The keyword <code>type</code> is followed by a float <code>
Patch_Type</code> which currently must be either 0 or 1. For type 0 only
the control points are retained within POV-Ray. This means that a minimal
amount of memory is needed but POV-Ray will need to perform many extra
calculations when trying to render the patch. Type 1 preprocesses the patch
into many subpatches. This results in a significant speedup in rendering at
the cost of memory.

{{#indexentry:u_steps, bicubic_patch}}
{{#indexentry:keyword, u_steps}}
{{#indexentry:v_steps, bicubic_patch}}
{{#indexentry:keyword, v_steps}}
{{#indexentry:flatness, bicubic_patch}}
{{#indexentry:keyword, flatness}}
The four parameters <code>type</code>, <code>flatness</code>, <code>
u_steps</code> and <code>v_steps</code> may appear in any order. Only
<code>type</code> is required. They are followed by 16 vectors (4 rows
of 4) that define the x, y, z coordinates of the 16 control points which
define the patch. The patch touches the four corner points <code>
<Point_1></code>, <code><Point_4></code>, 
<code><Point_13></code> and <code>
<Point_16></code> while the other 12 points pull and stretch the
patch into shape. The Bezier surface is enclosed by the convex hull formed by
the 16 control points, this is known as the convex hull property.

The keywords <code>u_steps</code> and <code>v_steps</code> are each followed
by integer values which tell how many rows and columns of triangles are the
minimum to use to create the surface, both default to 0. The maximum number of individual pieces
of the patch that are tested by POV-Ray can be calculated from the following:
pieces = 2^u_steps * 2^v_steps.

This means that you really should keep <code>u_steps</code> and <code>
v_steps</code> under 4. Most patches look just fine with <code>u_steps
3</code> and <code>v_steps 3</code>, which translates to 64 sub-patches (128
smooth triangles).

As POV-Ray processes the Bezier patch it makes a test of the current piece
of the patch to see if it is flat enough to just pretend it is a rectangle.
The statement that controls this test is specified with the <code>
flatness</code> keyword followed by a float. Typical flatness values range
from 0 to 1 (the lower the slower). The default if none is specified is
0.0.

If the value for flatness is 0 POV-Ray will always subdivide the patch to
the extend specified by <code>u_steps</code> and <code>v_steps</code>. If
flatness is greater than 0 then every time the patch is split, POV-Ray will
check to see if there is any need to split further.

There are both advantages and disadvantages to using a non-zero flatness.
The advantages include:

- If the patch is not very curved, then this will be detected and
POV-Ray will not waste a lot of time looking at the wrong pieces.

- If the patch is only highly curved in a couple of places, POV-Ray will keep
subdividing there and concentrate its efforts on the hard part.

The biggest disadvantage is that if POV-Ray stops subdividing at a
particular level on one part of the patch and at a different level on an
adjacent part of the patch there is the potential for cracking. This is
typically visible as spots within the patch where you can see through. How
bad this appears depends very highly on the angle at which you are viewing
the patch.


Like triangles, the bicubic patch is not meant to be generated by hand. These
shapes should be created by a special utility. You may be able to acquire
utilities to generate these shapes from the same source from which you
obtained POV-Ray. Here is an example:
<pre>
bicubic_patch {
type 0
flatness 0.01
u_steps 4
v_steps 4
<0, 0, 2>, <1, 0, 0>, <2, 0, 0>, <3, 0,-2>,
<0, 1 0>, <1, 1, 0>, <2, 1, 0>, <3, 1, 0>,
<0, 2, 0>, <1, 2, 0>, <2, 2, 0>, <3, 2, 0>,
<0, 3, 2>, <1, 3, 0>, <2, 3, 0>, <3, 3, -2>
}
</pre>

The triangles in a POV-Ray <code>bicubic_patch</code> are automatically
smoothed using normal interpolation but it is up to the user (or the
user's utility program) to create control points which smoothly stitch
together groups of patches.

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