Visual Comparison

The results of the algorithm can be measured by graphical analysis of a model at different stages. This analysis is the procedure that was used by William J. Schroeder, Jonathan A. Zarge and William E. Lorensen[#!shroeder!#] in their initial study. We will look at nine different models, each having interesting shapes and contours that will test the flexibility of the algorithm. For each of the models we take a snapshot look at several different stages in the decimation process.

The first stage is the original model, unaltered and freshly loaded into the program. The second stage will show the model after sixty percent of the vertices have been removed. The third stage will be after eighty percent, and the last stage will be after ninety percent. Along with the images will be information that shows exactly how many vertices have been removed and how long the process had taken.

The next set of images depicts the first test model test001.wrl in four levels of detail. The top left viewport has the original model, the top right has the model decimated at sixty percent, the bottom left has the model decimated at eighty percent, and the bottom right has the model decimated at ninety percent. This model is a three sided pyramid with an extra vertex on the bottom, so it initially has four vertices and six triangle polygons. After removing the only extraneous polygon it has the least amount of polygons, which is four. Therefore, at each sixty, eighty, and ninety, the model is the same (fully decimated), which means our program has properly recognized the corners and not removed them.

The first image, Figure , is a rendering of the solid model with no options enabled. The solid rendering shows how the models at each level of detail differ. In this case it fails to change the geometry of the model, since the extraneous vertex had a distance of 0 (zero) to the average plane (see discussions of our algorithm in 3.1 Design).

Figure: The model test001 rendered solid.

Figure is a rendering of the solid model with the wireframe option enabled. This image has an advantage over the previous image by showing the hidden lines (edges) that complete the model. With larger models it becomes more apparent how many vertices have been removed.

Figure: The model test001 rendered solid with wireframe lines to show edges.

Figure is a rendering of the model with various options enabled. The top left viewport has the original model with only points rendered. The top right viewport has the fully decimated model with triangle normals visible (the red lines). The bottom left viewport has the fully decimated model with only edges rendered. The bottom right viewport has the fully decimated model with only points rendered. The top left and bottom right viewports can be compared directly to show our program did indeed remove the only extraneous vertex.

Figure: The model test001 rendered with various options enabled.

The next set of images depicts the second test model test002.wrl in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). This model is a small two-by-two cube. This model initially has twenty-six vertices and forty-eight triangle polygons. The fully decimated model has eight vertices and twelve triangle polygons, making a perfect and maximally simplified cube.

The first image, Figure , is a rendering of the solid model with no options enabled. The solid rendering shows how the models at each level of detail differ.

Figure: The model test002 rendered solid.

Figure is a rendering of the solid model with the wireframe option enabled. This image has an advantage over the previous image by showing the hidden lines (edges) that complete the model. With larger models it becomes more apparent how many vertices have been removed.

Figure: The model test002 rendered solid with wireframe lines to show edges.

Figure is a rendering of the model with the show points option enabled. This image has an advantage over the previous image by showing the exact points that complete the model. With larger models it becomes more apparent how many vertices have been removed.

Figure: The model test002 rendered in points.

The next set of images depicts the third test model test003.wrl in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). This model is a single sided ten-by-ten plane. This model initially has 121 vertices and 200 triangle polygons. The fully decimated model has 40 vertices and 38 triangle polygons. The ideal solution for a single sided plane is four points and two polygons, but our program detects boundary edges the same way as it detects corners, so they are not removed.

Figure: The model test003 rendered solid.

Figure: The model test003 rendered solid with wireframe lines to show edges.

Figure: The model test003 rendered in points.

The next set of images depicts the fourth test model test004.wrl in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). This model is a large ten-by-ten cube. This model initially has 602 vertices and 1200 triangle polygons. The fully decimated model has eight vertices and twelve triangle polygons. The result of fully decimating this model is a perfect, and maximally simplified cube, with eight vertices.

Figure: The model test004 rendered solid.

Figure: The model test004 rendered solid with wireframe lines to show edges.

Figure: The model test004 rendered in points.

The next set of images depicts the fifth test model test005.wrl in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). This model is a hollow cylinder (a tube). This model initially has 528 vertices and 1056 triangle polygons. The model has no corners so it can be completely removed from the scene when "fully" decimated. Remember: we define a corner as either a boundary edge or a point that creates an angle greater than 60 degrees at all neighbors.

Figure: The model test005 rendered solid.

Figure: The model test005 rendered solid with wireframe lines to show edges.

Figure: The model test005 rendered in points.

The next set of images depicts the sixth through eighth test models in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). Model test006 is a squashed four sided triangle pyramid (a dome). This model initially has 2402 vertices and 4800 triangle polygons. The fully decimated model has 449 vertices and 894 triangle polygons. Model test007 is a washer that has been distorted with noise and wave commands in 3D Studio Max. This model initially has 9648 vertices and 19200 triangle polygons. The fully decimated model has 1072 vertices and 2048 triangle polygons. Model test008 is a box that has been stretched. This model initially has 14402 vertices and 28800 triangle polygons. The fully decimated model has twelve vertices and twenty triangle polygons.

Figure: The model test006 rendered solid.

Figure: The model test006 rendered solid with wireframe lines to show edges.

Figure: The model test006 rendered in points.

Figure: The model test007 rendered solid.

Figure: The model test007 rendered solid with wireframe lines to show edges.

Figure: The model test007 rendered in points.

Figure: The model test008 rendered solid.

Figure: The model test008 rendered solid with wireframe lines to show edges.

Figure: The model test008 rendered in points.

The next set of images depicts the ninth test model test009.wrl in four levels of detail. The viewports are arranged in the exact same manner as the last set of images (original, sixty percent, eighty percent, ninety percent). This model is a 3D visualization created from photographs of a real scene, given to us by WPI professor Mark Stevens. This model initially has 57570 vertices and 114880 triangle polygons. The fully decimated model has 1723 vertices and 3180 triangle polygons.

Figure: The model test009 rendered solid.

Figure is the same rendering as the previous image, with the exception that the smoothing option has been enabled.

Figure: The model test009 rendered solid with OpenGL point smoothing enabled.

Figure: The model test009 rendered solid with wireframe lines to show edges.

Figure is a rendering of the model with the show points option enabled. This image has an advantage over the previous image by showing the exact points that complete the model. With larger models it becomes more apparent how many vertices have been removed.

Figure: The model test009 rendered in points.

We will now examine the results for the test009 model in detail. The viewport is located on the face of the person on the left, facing the model.

Figure is the rendering of the model at the same levels of detail as all the previous image series (original, 60, 80, 90 percent). When we zoom into this specific location of the model, we see how the algorithm is modifying the model.

Figure: The model test009 rendered solid (detail).

Figure is the image of the same models in Figure , but with the smoothing option enabled. When we compare this figure with Figure we see that this makes the models appear much closer in appearance to the original model, which is in the top left viewport in both figures. Most applications of 3D graphics render with smoothing enabled, so this indicates that our program can yield good results that can be indistinguishable from the original large models even after ninety percent of the vertices have been removed.

Figure: The model test009 rendered solid with OpenGL point smoothing enabled (detail).

Figure shows the same image as Figure , with the exception that the wireframe option is enabled. We clearly see how many polygons have been removed in the bottom right viewport (90 percent decimated).

Figure: The model test009 rendered solid with wireframe lines to show edges (detail).