POV-Ray : Documentation : 1.3.2.2 Mesh2 Object
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1.3.2.1 Mesh Object   1.3.2.3 Polygon Object

1.3.2.2 Mesh2 Object

The mesh2 is a representation of a mesh, that is much more like POV-Ray's internal mesh representation than the standard mesh. As a result, it parses faster and it file size is smaller.

Due to its nature, mesh2 is not really suitable for building meshes by hand, it is intended for use by modelers and file format converters. An other option is building the meshes by macros. Yet, to understand the format, we will do a small example by hand and go through all options.

to be written as mesh2

We will turn the mesh sketched above into a mesh2 object. The mesh is made of 8 triangles, each with 3 vertices, many of these vertices are shared among the triangles. This can later be used to optimize the mesh. First we will set it up straight forward.

In mesh2 all the vertices are listed in a list named vertex_vectors{}. A second list, face_indices{}, tells us how to put together three vertices to create one triangle, by pointing to the index number of a vertex. All lists in mesh2 are zero based, the number of the first vertex is 0. The very first item in a list is the amount of vertices, normals or uv_vectors it contains. mesh2 has to be specified in the order VECTORS..., LISTS..., INDICES....

Lets go through the mesh above, we do it counter clockwise. The total amount of vertices is 24 (8 triangle * 3 vertices).

mesh2 {
   vertex_vectors {
      24,
      ...

Now we can add the coordinates of the vertices of the first triangle:

mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>
      ..

Next step, is to tell the mesh how the triangle should be created; There will be a total of 8 face_indices (8 triangles). The first point in the first face, points to the first vertex_vector (0: <0,0,0>), the second to the second (1: <0.5,0,0>), etc...

mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>
      ...
   }
   face_indices {
      8, 
      <0,1,2> 
      ...

The complete mesh:

mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>, //1
      <0.5,0,0>, <1,0,0>, <0.5,0.5,0>, //2
      <1,0,0>, <1,0.5,0>, <0.5,0.5,0>, //3
      <1,0.5,0>, <1,1,0>, <0.5,0.5,0>, //4
      <1,1,0>, <0.5,1,0>, <0.5,0.5,0>, //5
      <0.5,1,0>, <0,1,0>, <0.5,0.5,0>, //6
      <0,1,0>, <0,0.5,0>, <0.5,0.5,0>, //7
      <0,0.5,0>, <0,0,0>, <0.5,0.5,0>  //8
   }
   face_indices {
      8, 
      <0,1,2>,    <3,4,5>,       //1 2
      <6,7,8>,    <9,10,11>,     //3 4
      <12,13,14>, <15,16,17>,    //5 6
      <18,19,20>, <21,22,23>     //7 8
   }
   pigment {rgb 1}
}

As mentioned earlier, many vertices are shared by triangles. We can optimize the mesh by removing all duplicate vertices but one. In the example this reduces the amount from 24 to 9.

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      /*as 1*/ <1,0,0>,   /*as 2*/
      /*as 3*/ <1,0.5,0>, /*as 2*/
      /*as 4*/ <1,1,0>,   /*as 2*/
      /*as 5*/ <0.5,1,0>, /*as 2*/
      /*as 6*/ <0,1,0>,   /*as 2*/
      /*as 7*/ <0,0.5,0>, /*as 2*/
      /*as 8*/ /*as 0*/   /*as 2*/
   }
   ...
   ...

Next step is to rebuild the list of face_indices, as they now point to indices in the vertex_vector{} list that do not exist anymore.

   ...
   ...
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   pigment {rgb 1}
}
1.3.2.2.1 Smooth triangles and mesh2

In case we want a smooth mesh, the same steps we did also apply to the normals in a mesh. For each vertex there is one normal vector listed in normal_vectors{}, duplicates can be removed. If the number of normals equals the number of vertices then the normal_indices{} list is optional and the indexes from the face_indices{} list are used instead.

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>, <0,0.5,0>   
   }
   normal_vectors {
      9,
     <-1,-1,0>,<0,-1,0>, <0,0,1>,
      /*as 1*/ <1,-1,0>, /*as 2*/
      /*as 3*/ <1,0,0>,  /*as 2*/
      /*as 4*/ <1,1,0>,  /*as 2*/
      /*as 5*/ <0,1,0>,  /*as 2*/
      /*as 6*/ <-1,1,0>, /*as 2*/
      /*as 7*/ <-1,0,0>, /*as 2*/
      /*as 8*/ /*as 0*/  /*as 2*/ 
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   pigment {rgb 1}
}

When a mesh has a mix of smooth and flat triangles a list of normal_indices{} has to be added, where each entry points to what vertices a normal should be applied. In the example below only the first four normals are actually used.

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   normal_vectors {
      9,
      <-1,-1,0>, <0,-1,0>, <0,0,1>,
      <1,-1,0>, <1,0,0>, <1,1,0>,
      <0,1,0>, <-1,1,0>, <-1,0,0>
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   normal_indices {
      4, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>
   }
   pigment {rgb 1}
}
1.3.2.2.2 UV mapping and mesh2

uv_mapping is a method of 'sticking' 2D textures on an object in such a way that it follows the form of the object. For uv_mapping on triangles imagine it as follows; First you cut out a triangular section of a texture form the xy-plane. Then stretch, shrink and deform the piece of texture to fit to the triangle and stick it on.

Now, in mesh2 we first build a list of 2D-vectors that are the coordinates of the triangular sections in the xy-plane. This is the uv_vectors{} list. In the example we map the texture from the rectangular area <-0.5,-0.5>, <0.5,0.5> to the triangles in the mesh. Again we can omit all duplicate coordinates

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   uv_vectors {
      9
     <-0.5,-0.5>,<0,-0.5>,  <0,0>,
      /*as 1*/   <0.5,-0.5>,/*as 2*/
      /*as 3*/   <0.5,0>,   /*as 2*/
      /*as 4*/   <0.5,0.5>, /*as 2*/
      /*as 5*/   <0,0.5>,   /*as 2*/
      /*as 6*/   <-0.5,0.5>,/*as 2*/
      /*as 7*/   <-0.5,0>,  /*as 2*/
      /*as 8*/   /*as 0*/   /*as 2*/       
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   uv_mapping
   pigment {wood scale 0.2}
}

Just as with the normal_vectors, if the number of uv_vectors equals the number of vertices then the uv_indices{} list is optional and the indices from the face_indices{} list are used instead.

In contrary to the normal_indices list, if the uv_indices list is used, the amount of indices should be equal to the amount of face_indices. In the example below only 'one texture section' is specified and used on all triangles, using the uv_indices.

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   uv_vectors {
      3
      <0,0>, <0.5,0>, <0.5,0.5>    
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   uv_indices {
      8, 
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>
   }
   uv_mapping
   pigment {gradient x scale 0.2}
}
1.3.2.2.3 A separate texture per triangle

By using the texture_list it is possible to specify a texture per triangle or even per vertex in the mesh. In the latter case the three textures per triangle will be interpolated. To let POV-Ray know what texture to apply to a triangle, the index of a texture is added to the face_indices list, after the face index it belongs to.

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>   
      <0.5,1,0>, <0,1,0>, <0,0.5,0> 
   }
   texture_list {
      2,
      texture{pigment{rgb<0,0,1>}}
      texture{pigment{rgb<1,0,0>}}
   }
   face_indices {
      8, 
      <0,1,2>,0,  <1,3,2>,1,
      <3,4,2>,0,  <4,5,2>,1,
      <5,6,2>,0,  <6,7,2>,1,
      <7,8,2>,0,  <8,0,2>,1
   }
}

To specify a texture per vertex, three texture_list indices are added after the face_indices

mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>   
      <0.5,1,0>, <0,1,0>, <0,0.5,0> 
   }
   texture_list {
      3,
      texture{pigment{rgb <0,0,1>}}
      texture{pigment{rgb 1}}
      texture{pigment{rgb <1,0,0>}}
   }
   face_indices {
      8, 
      <0,1,2>,0,1,2,  <1,3,2>,1,0,2,
      <3,4,2>,0,1,2,  <4,5,2>,1,0,2,
      <5,6,2>,0,1,2,  <6,7,2>,1,0,2,
      <7,8,2>,0,1,2,  <8,0,2>,1,0,2
   }
}

Assigning a texture based on the texture_list and texture interpolation is done on a per triangle base. So it is possible to mix triangles with just one texture and triangles with three textures in a mesh. It is even possible to mix in triangles without any texture indices, these will get their texture from a general texture statement in the mesh2. uv_mapping is supported for texturing using a texture_list.

1.3.2.1 Mesh Object   1.3.2.3 Polygon Object


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