Reference:Prism - Revision history

Jholsenback: added caveat and removed obsolete passage

2017-10-01T14:39:11Z

added caveat and removed obsolete passage

Jholsenback: corrected link issue

2016-07-17T14:00:54Z

corrected link issue

Jholsenback: user contributed update

2016-06-06T10:04:32Z

user contributed update

Jholsenback: consistency

2016-05-31T17:06:34Z

consistency

Jholsenback: clarification

2016-05-28T14:01:06Z

clarification

Jholsenback: clean up and user contributed additions

2016-05-26T23:52:01Z

clean up and user contributed additions

Show changes

Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:08:36Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:27:00Z

1 revision: Initial Load (TF)

New page

[[Category:Objects]]
[[Category:Finite Solid Primitives]]
{{#indexentry:prism, keyword}}
{{#indexentry:keyword, prism}}
{{#indexentry:open, prism}}
{{#indexentry:keyword, open}}
{{#indexentry:linear_spline, prism}}
{{#indexentry:keyword, linear_spline}}
{{#indexentry:quadratic_spline, prism}}
{{#indexentry:keyword, quadratic_spline}}
{{#indexentry:cubic_spline, prism}}
{{#indexentry:keyword, cubic_spline}}
{{#indexentry:bezier_spline, prism}}
{{#indexentry:keyword, bezier_spline}}
{{#indexentry:sturm, prism}}
{{#indexentry:keyword, sturm}}
The <code>prism</code> is an object generated by specifying one or more two-dimensional, closed curves in the x-z plane and sweeping them along y axis. These curves are defined by a set of points which are connected by linear, quadratic, cubic or bezier splines. The syntax for the prism is:
<pre>
PRISM:
prism {
[PRISM_ITEMS...] Height_1, Height_2, Number_Of_Points,
<Point_1>, <Point_2>, ... <Point_n>
[ open ] [PRISM_MODIFIERS...]
}
PRISM_ITEM:
linear_spline | quadratic_spline | cubic_spline |
bezier_spline | linear_sweep | conic_sweep
PRISM_MODIFIER:
sturm | OBJECT_MODIFIER
</pre>

{{#indexentry:default values, prism}}
Prism default values:

<pre>
SPLINE_TYPE : linear_spline
SWEEP_TYPE : linear_sweep
sturm : off
</pre>

{{#indexentry:linear_sweep, prism}}
{{#indexentry:keyword, linear_sweep}}
The first items specify the spline type and sweep type. The defaults if
none is specified is <code>linear_spline</code> and <code>
linear_sweep</code>. This is followed by two float values <code>
Height_1</code> and <code>Height_2</code> which are the y
coordinates of the top and bottom of the prism. This is followed by a float
value specifying the number of 2-D points you will use to define the prism.
(This includes all control points needed for quadratic, cubic and bezier
splines). This is followed by the specified number of 2-D vectors which
define the shape in the x-z plane.

The interpretation of the points depends on the spline type. The prism
object allows you to use any number of sub-prisms inside one prism statement
(they are of the same spline and sweep type). Wherever an even number of
sub-prisms overlaps a hole appears.
Note: You need not have multiple sub-prisms and they need not overlap as these examples do.

In the <code>linear_spline</code> the first point specified is the start of
the first sub-prism. The following points are connected by straight lines. If
you specify a value identical to the first point, this closes the sub-prism
and next point starts a new one. When you specify the value of that
sub-prism's start, then it is closed. Each of the sub-prisms has to be
closed by repeating the first point of a sub-prism at the end of the
sub-prism's point sequence. In this example, there are two rectangular
sub-prisms nested inside each other to create a frame.
<pre>
prism {
linear_spline
0, 1, 10,
<0,0>, <6,0>, <6,8>, <0,8>, <0,0>, //outer rim
<1,1>, <5,1>, <5,7>, <1,7>, <1,1> //inner rim
}
</pre>

The last sub-prism of a linear spline prism is automatically closed - just
like the last sub-polygon in the polygon statement - if the first and last
point of the sub-polygon's point sequence are not the same. This make it
very easy to convert between polygons and prisms. Quadratic, cubic and bezier
splines are never automatically closed.

In the <code> quadratic_spline</code>, each sub-prism needs an additional
control point at the beginning of each sub-prisms' point sequence to
determine the slope at the start of the curve. The first point specified is
the control point which is not actually part of the spline. The second point
is the start of the spline. The sub-prism ends when this second point is
duplicated. The next point is the control point of the next sub-prism. The
point after that is the first point of the second sub-prism. Here is an
example:
<pre>
prism {
quadratic_spline
0, 1, 12,
<1,-1>, <0,0>, <6,0>, //outer rim; <1,-1> is control point and
<6,8>, <0,8>, <0,0>, //<0,0> is first & last point
<2,0>, <1,1>, <5,1>, //inner rim; <2,0> is control point and
<5,7>, <1,7>, <1,1> //<1,1> is first & last point
}
</pre>

In the <code>cubic_spline</code>, each sub-prism needs two additional
control points -- one at the beginning of each sub-prisms' point sequence
to determine the slope at the start of the curve and one at the end. The
first point specified is the control point which is not actually part of the
spline. The second point is the start of the spline. The sub-prism ends when
this second point is duplicated. The next point is the control point of the
end of the first sub-prism. Next is the beginning control point of the next
sub-prism. The point after that is the first point of the second
sub-prism.

Here is an example:
<pre>
prism {
cubic_spline
0, 1, 14,
<1,-1>, <0,0>, <6,0>, //outer rim; First control is <1,-1> and
<6,8>, <0,8>, <0,0>, //<0,0> is first & last point.
<-1,1>, //Last control of first spline is <-1,1>
<2,0>, <1,1>, <5,1>, //inner rim; First control is <2,0> and
<5,7>, <1,7>, <1,1>, //<1,1> is first & last point
<0,2> //Last control of first spline is <0,2>
}
</pre>

{{#indexentry:conic_sweep, prism}}
{{#indexentry:keyword, conic_sweep}}
The <code>bezier_spline</code> is an alternate kind of cubic spline.
Points 1 and 4 specify the end points of a segment and points 2 and 3 are
control points which specify the slope at the endpoints. Points 2 and 3 do
not actually lie on the spline. They adjust the slope of the spline. If you
draw an imaginary line between point 1 and 2, it represents the slope at
point 1. It is a line tangent to the curve at point 1. The greater the
distance between 1 and 2, the flatter the curve. With a short tangent the
spline can bend more. The same holds true for control point 3 and endpoint 4.
If you want the spline to be smooth between segments, point 3 and 4 on one
segment and point 1 and 2 on the next segment must form a straight line and
point 4 of one segment must be the same as point one on the next segment.

By default linear sweeping is used to create the prism, i.e. the prism's
walls are perpendicular to the x-z-plane (the size of the curve does not
change during the sweep). You can also use <code>conic_sweep</code> that
leads to a prism with cone-like walls by scaling the curve down during the
sweep.

Like cylinders the prism is normally closed. You can remove the caps on the
prism by using the <code>open</code> keyword. If you do so you should not
use it with CSG because the results may get wrong.

For an explanation of the spline concept read the description of the
[[Reference:Lathe|Lathe]] object. Also see the tutorials on
[[Documentation:Tutorial Section 3#Lathe Object|Lathe]] and [[Documentation:Tutorial Section 3#Prism Object|Prism]] objects.

{{#indexentry:sturm, prism}}
{{#indexentry:keyword, sturm}}
The <code> sturm</code> keyword specifies the slower but more accurate
Sturmian root solver which may be used with the cubic or bezier spline prisms
if the shape does not render properly. The linear and quadratic spline prisms
do not need the Sturmian root solver.

@@ Line 85: / Line 85: @@
 <p>By default linear sweeping is used to create the prism, that is, the prism's walls are perpendicular to the x-z plane. The size of the curve does not change during the sweep. You can also use <code>conic_sweep</code> that leads to a prism with cone-like walls by scaling the curve down during the sweep.</p>
 <p>Like cylinders the prism is normally closed. You can remove the caps on the prism by using the <code>open</code> keyword. If you do, you should not use it in CSG operations, because the result may not be as expected.</p>
-<p>The surface normal determination for prism sides depends upon the order in which the splines points are specified.  Prism ends have normals which face outward at one end and inward at the other end.  The following code will render sides with the color Red on the outside and the color Blue on the inside.</p>
+<p>The surface normal determination for prism sides depends upon the order in which the splines points are specified.  Prism ends have normals which face outward at one end and inward at the other end. For <code>interior_texture</code> to work as expected, the outline of the underlying 2D shape must be specified in counter-clockwise order, except for holes which must be specified in clockwise order, and they must not self-intersect.</p>
 <pre>
 #declare Prism_InitialOrder = prism {
@@ Line 108: / Line 110: @@
 </pre>
 <p>The actual normal determination is more complicated for complex splines. If the surface normal is important to the visual result, it is best to check how the prism is being rendered by testing with substantially different inside and outside textures.</p>
 {{#indexentry:sturm, prism}}
 {{#indexentry:keyword, sturm}}

@@ Line 111: / Line 111: @@
 {{#indexentry:sturm, prism}}
 {{#indexentry:keyword, sturm}}
-<p>If additional accuracy is required you can add the <code>[[Reference:Sturm_Object_Modifier|sturm]]</code> object modifier.</p>
+<p>If additional accuracy is required you can add the <code>[[Reference:Sturm Object Modifier|sturm]]</code> object modifier.</p>
 <p>For an explanation of the spline concept read the description for the <!--<linkto "Lathe">Lathe</linkto>--->[[Reference:Lathe|Lathe]] object.</p>
 <p>See also the tutorials on [[Documentation:Tutorial Section 3#Lathe Object|Lathe]] and [[Documentation:Tutorial Section 3#Prism Object|Prism]] objects.</p>

@@ Line 112: / Line 112: @@
 {{#indexentry:sturm, prism}}
 {{#indexentry:keyword, sturm}}
-<p>The <code> sturm</code> keyword specifies the slower but more accurate Sturmian root solver which may be used with the cubic or bezier spline prisms if the shape does not render properly. The linear and quadratic spline prisms do not need the Sturmian root solver.</p>
+<p>If additional accuracy is required you can add the <code>[[Reference:Sturm_Object_Modifier|sturm]]</code> object modifier.</p>
 <p>For an explanation of the spline concept read the description for the <!--<linkto "Lathe">Lathe</linkto>--->[[Reference:Lathe|Lathe]] object.</p>
 <p>See also the tutorials on [[Documentation:Tutorial Section 3#Lathe Object|Lathe]] and [[Documentation:Tutorial Section 3#Prism Object|Prism]] objects.</p>

@@ Line 85: / Line 85: @@
 <p>By default linear sweeping is used to create the prism, that is, the prism's walls are perpendicular to the x-z plane. The size of the curve does not change during the sweep. You can also use <code>conic_sweep</code> that leads to a prism with cone-like walls by scaling the curve down during the sweep.</p>
 <p>Like cylinders the prism is normally closed. You can remove the caps on the prism by using the <code>open</code> keyword. If you do, you should not use it in CSG operations, because the result may not be as expected.</p>
 <p>The surface normal determination for prism sides depends upon the order in which the splines points are specified. Prism ends have normals which always face outward. The following code, where the linear spline point order is <em>counter-clockwise</em> in the x-z plane, will render sides with the color Red on the outside and the color Blue on the inside. The prism ends will also be Red on the outside and Blue on the inside.</p>
 <pre>

@@ Line 2: / Line 2: @@
 [[Category:Finite Solid Primitives]]
 {{#indexentry:prism, keyword}}
 {{#indexentry:keyword, prism}}
 {{#indexentry:open, prism}}
 {{#indexentry:keyword, open}}
 {{#indexentry:linear_spline, prism}}
 {{#indexentry:keyword, linear_spline}}
 {{#indexentry:quadratic_spline, prism}}
 {{#indexentry:keyword, quadratic_spline}}
 {{#indexentry:cubic_spline, prism}}
 {{#indexentry:keyword, cubic_spline}}
 {{#indexentry:bezier_spline, prism}}
 {{#indexentry:keyword, bezier_spline}}
 {{#indexentry:sturm, prism}}
 {{#indexentry:keyword, sturm}}
@@ Line 38: / Line 38: @@
 </pre>
 {{#indexentry:linear_sweep, prism}}
 {{#indexentry:keyword, linear_sweep}}
 <p>The first items specify the spline type and sweep type. The defaults if none is specified is <code>linear_spline</code> and <code> linear_sweep</code>. This is followed by two float values <em><code>Height_1</code></em> and <em> <code>Height_2</code></em> which are the y
 coordinates of the top and bottom of the prism. This is followed by a float value specifying the number of 2-D points you will use to define the prism.This includes all control points needed for quadratic, cubic and bezier splines. This is followed by the specified number of 2-D vectors which define the shape in the x-z plane.</p>
@@ Line 60: / Line 60: @@
    quadratic_spline
 , 1, 12,
    &lt;1,-1&gt;, &lt;0,0&gt;, &lt;6,0&gt;, //outer rim; &lt;1,-1&gt; is control point and
    &lt;6,8&gt;, &lt;0,8&gt;, &lt;0,0&gt;,  //&lt;0,0&gt; is first &amp; last point
    &lt;2,0&gt;, &lt;1,1&gt;, &lt;5,1&gt;,  //inner rim; &lt;2,0&gt; is control point and
    &lt;5,7&gt;, &lt;1,7&gt;, &lt;1,1&gt;   //&lt;1,1&gt; is first &amp; last point
+   }
@@ Line 75: / Line 75: @@
    &lt;6,8&gt;, &lt;0,8&gt;, &lt;0,0&gt;,  //&lt;0,0&gt; is first &amp; last point.
    &lt;-1,1&gt;,                           //Last control of first spline is &lt;-1,1&gt;
    &lt;2,0&gt;, &lt;1,1&gt;, &lt;5,1&gt;,  //inner rim; First control is &lt;2,0&gt; and
    &lt;5,7&gt;, &lt;1,7&gt;, &lt;1,1&gt;,  //&lt;1,1&gt; is first &amp; last point
    &lt;0,2&gt;                             //Last control of first spline is &lt;0,2&gt;
@@ Line 85: / Line 85: @@
 <p>By default linear sweeping is used to create the prism, that is, the prism's walls are perpendicular to the x-z plane. The size of the curve does not change during the sweep. You can also use <code>conic_sweep</code> that leads to a prism with cone-like walls by scaling the curve down during the sweep.</p>
 <p>Like cylinders the prism is normally closed. You can remove the caps on the prism by using the <code>open</code> keyword. If you do, you should not use it in CSG operations, because the result may not be as expected.</p>
-<p class="Note"><strong>Note:</strong> The use of <em>clockwise</em> and <em>counter-clockwise</em> in the following examples should not be taken imply any notion of [[Reference:Camera#Handedness|handedness]].</p>
+<p>The surface normal determination for prism sides depends upon the order in which the splines points are specified.  Prism ends have normals which face outward at one end and inward at the other end.  The following code will render sides with the color Red on the outside and the color Blue on the inside.</p>
 <pre>
-#declare Prism_CounterClockwise = prism {
+#declare Prism_InitialOrder = prism {
      linear_spline
      linear_sweep
@@ Line 97: / Line 96: @@
+}
 </pre>
-<p>While the following example, where the point order for the linear spine is <em>clockwise</em> in the x-z plane, will render sides inside-out with the color Blue on the outside and the color Red on the inside. Surface normals for the prism ends are unchanged.</p>
+<p>While the following example will render sides inside-out with the color Blue on the outside and the color Red on the inside. Surface normals for the prism ends are unchanged.</p>
 <pre>
-#declare Prism_Clockwise = prism {
+#declare Prism_ReverseOrder = prism {
      linear_spline
      linear_sweep
@@ Line 108: / Line 107: @@
+}
 </pre>
-<p>The actual normal determination is more complicated than <em>clockwise</em> vs <em>counter-clockwise</em> orientation for complex splines. If the surface normal is important to the visual result, it is best to check how the prism is being rendered by testing with substantially different inside and outside textures.</p>
+<p>The actual normal determination is more complicated for complex splines. If the surface normal is important to the visual result, it is best to check how the prism is being rendered by testing with substantially different inside and outside textures.</p>
-<p>There is presently a inconsistency with the bezier spline mode of the prism in that the point order with respect to side surface normals is reversed from all other prism spline types. To match the end normals, for all but the bezier spline, the point list should be in <em>counter-clockwise</em> order in the x-z plane, while for the bezier spline, the point order must be <em>clockwise</em>. The behavior of the bezier spline prism will likely be aligned with the other spline types in a later release.</p>
+<p>There is presently a inconsistency with the bezier spline mode of the prism in that the point order with respect to side surface normals is reversed from all other prism spline types. The behavior of the bezier spline prism will likely be aligned with the other spline types in a later release. Further end behavior may be made consistent for all spline types.</p>
 {{#indexentry:sturm, prism}}
 {{#indexentry:keyword, sturm}}

← Older revision	Revision as of 19:08, 15 March 2012
(No difference)