Overview

Requirements

Surface of Revolution

A surface of revolution is a surface created by rotating a curve around an axis. The interface for editing the curve is already provided. Your task is to implement the surface of revolution algorithm given the samples of points on the curve and the number of radial subdivisions. Typically, to describe a mesh you only need vertex positions and a triangle list of how the vertices are connected. In this project however, you are also required to compute the vertex normal and the texture coordinate (UV coordinates) for each vertex.

Program Overview

Go to the SurfaceOfRevolution scene and hit play. In “Play” mode, you will see a working curve editor on your left and some options on the top-right. You should change the resolution to Full HD or any with 16:9 aspect ratio for the UI to display correctly. Right now, you can only create and delete control points of the curve. Once your code is done, you will be able to click ‘Create’ and the output mesh will appear on the lower-right of the screen.

To construct a curve, click anywhere on the graph. The control point will appear on the screen. This graph is on the xy-plane, and the curve you created will be automatically reflected with respect to the y-axis for visualization purposes.

There are several options for the curve and the output mesh:

• Interpolation: determines the interpolation method between adjacent control points. Two options provided are: Catmull-Rom (smooth), and Linear. Note that for the Catmull-Rom option, you will need at least 4 control points whereas the linear option needs at least two.
• Density: the number of samples between two adjacent control points. More density means the curve will look smoother.
• Subdivision: the number of radial subdivisions. This is the option passed to your function. More subdivisions means the mesh will look smoother around the vertical axis.
• Wrap: whether to close the curve (basically, to connect the last control point to the first)

After changing these options, you will need to click Create again for the change to reflect on your output mesh. We suggest you use the default settings while you are trying to debug your code.

We provide four viewing options of the output mesh (top-right dropdown) to aid your debugging: standard, wireframe, normal visualization, and textured. You can use the wireframe to see the actual triangle of your mesh. The normal visualization shows different colors based on the direction of the normal at that point. This mode is helpful to determine if you get the vertex normals correct. The textured shows your mesh with the textured material. This will help determine if you get your UV coordinates right.

Once you have created a surface, you can click Save to save the control points to a text file, and you can use Load to load that text file back to get the exact same control points. You can also Export the model as a .asset file so that it can be used in the next part of the project or one of your own.

Surface of Revolution Implementation

To complete this part, fill out the ComputeMeshData() function in the SurfaceOfRevolution.cs.

Your function will use the following variables as inputs:

• curvePoints: the list of sampled points on the curve
• subdivisions: the number of radial subdivisions

Your function will compute the following, which will be used to generate and visualize the output mesh:

• vertices: a list of Vector3 containing the vertex positions.
• normals: a list of Vector3 containing the vertex normals. The normal should be pointing out of the mesh.
• UVs: a list of Vector2 containing the texture coordinates of each vertex
• triangles: an integer array containing vertex indices (of the vertices list). The first three elements describe the first triangle, the fourth to sixth elements describe the second triangle, and so on. The vertex must be oriented counterclockwise when viewed from the outside.

Note that since vertices, normals, UVs are per-vertex information, they will have the same size: the number of vertices.

Texture mapping allows you to “wrap” an image around your model by mapping points on the texture to the vertices of your model. For each vertex, you indicate the coordinate in the texture space that the vertex should be mapped to as a 2D pair (U, V) where U and V range from 0 to 1. For example, if the UV coordinates of vertex 8 is (0.5, 0.5), The very center pixel of the texture will be mapped to vertex 8. Unity and the shader will automatically interpolate the UV coordinate inside the faces based on the UV coordinate of the vertices. You may create a copy of the first set of vertices to allow the UVs to map to the entire texture.

We recommend you first start working on computing the vertices and triangles. Then, move on to normals, and lastly the UVs.

Using Different Textures

If you want to use a different texture, you will need to do the following:

1. Import an image file into your scene by drag-and-dropping the image into the Assets folders under the Project tab.
2. Select Assets/Resources/TexturedMat material, then navigate to the Inspector pane to set its Albedo property under Main Maps to be the image file.

Using Different Textures

To verify the correctness of your implementation, follow these steps:

1. Select Load, then navigate to the ControlPoints folder and choose our provided file sample1.txt, sample2.txt, etc.
2. After the points are loaded, click Create to draw a surface of revolution.
3. Do the same for the solution program. Observe if the output from your implementation is similar to the solution. Change to a different viewing mode and then compare your results with the solution.