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A cube has 8 unique vertices. Is it true that each of these 8 vertex normals (unit vectors) is making 135 degree angle to each of the edges which shares that vertex? And the vertex normal pointing outward/out of the cube? Your answer should be technically correct. Or it depends on how the cube is defined (drawn) like using triangle strips or indices that define 2 triangles for each side of the cube? The purpose of the vertex normal is smooth shading and lighting in OpenGL ES application.
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Since the normal will be the same for two surfaces that are coplanar, you will only need 6 surface normals. However, often, it's the case that normals are expected to be defined per vertex, in which case you'll need 36 (one for each vertex of each triangle on each face of the cube).
The algorithm to compute such vertex normals is as follows: First, allocate an array of normals, one for each vertex in the mesh, and initialize them to zero (Point3( 0,0,0)). Then for each face, compute its face normal, and add it into each of the three vertex normals that the face contributes to.
The normal to the plane is given by the cross product n=(r−b)×(s−b).
Vertex normals (sometimes called pseudo-normals) are values stored at each vertex that are most commonly used by a renderer to determine the reflection of lighting or shading models, such as phong shading. For example, the normal of a surface is used to calculate which direction light reflects off this surface.
If the cube is defined by 8 unique vertices, then the normals will likely be making a 135 degree angle to each edge, as you mentioned.
However, a cube is often defined using 24 vertices for exactly this reason. This allows you to have vertex normals that are perpendicular to each face, by "duplicating" vertices at each corner. Defining a cube this way is, effectively, just defining 6 individual faces, each pointing outwards appropriately.
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There is no point in smoothing the cube with 8 vertices in order to make it look like a sphere. You'll get an extremely ugly sphere this way. The only reasonable way to draw the cube is using 24 unique vertices.
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