Compute ParametricGeometry normals from tangent vectors #11056
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src/geometries/ParametricGeometry.js
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| // approximate tangent plane vectors via central difference | ||
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| pu.subVectors( func( u + EPS, v ), func( u - EPS, v ) ); | ||
| pv.subVectors( func( u, v + EPS ), func( u, v - EPS ) ); |
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Should the Vector3s returned by func be .cloneed here in case the Vector3s actually reference the same object? Or is there a better way to do this?
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func normally returns a new instance of Vector3, see https://github.com/mrdoob/three.js/blob/dev/examples/js/ParametricGeometries.js
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@Mugen87 Actually, there should be no reason to instantiate 4 * slices * stacks Vector3's when using central differences. We could add an optionalTarget to func() and reuse just two instances.
var result = optionalTarget || new THREE.Vector3();
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return result.set( x, y, z );There was a problem hiding this comment.
Sounds reasonable. We can also adjust some entities in THREE.ParametricGeometries so they use the optionalTarget. But let's do this in a separate PR, okay?
@jaxry Are you interested in doing this 😉 ?
jaxry
changed the title
There is no need to override |
src/geometries/ParametricGeometry.js
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| @@ -72,6 +77,16 @@ function ParametricBufferGeometry( func, slices, stacks ) { | |||
| var p = func( u, v ); | |||
| vertices.push( p.x, p.y, p.z ); | |||
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| // approximate tangent plane vectors via central difference | |||
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| pu.subVectors( func( u + EPS, v ), func( u - EPS, v ) ); | |||
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Is func( u, v ) guaranteed to be well-defined for values of u, v outside [ 0, 1 ] ?
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That's a good point! According to the implementation of func(), values outside [ 0, 1 ] can be problematic.
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Then, use non-centered differences with a special case for the edge. By reusing p, only two additional calls are needed.
src/geometries/ParametricGeometry.js
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| // cross product of tangent plane vectors returns surface normal | ||
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| normal.crossVectors( pu, pv ); |
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normal.crossVectors( pu, pv ).normalize();
src/geometries/ParametricGeometry.js
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| // generate normals | ||
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| this.computeVertexNormals(); | ||
| this.normalizeNormals(); |
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Yes, This is a good change as long as |
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Thanks for the feedback. I implemented your suggestions. |
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Thanks! |
The ParametricGeometry class generates vertex normals as usual from the geometry's faces. However, this method leads to incorrectly computed normals for closed parametric surfaces. Where two ends of a surface meet, a seam is created since the positions along the edge are shared, but the indices of the geometry aren't.
For example, here you can see two seams on this torus created using ParametricGeometry:
This PR attempts to solve the problem. These seams are removed if you calculate the normals from the parametric equation itself.
By approximating tangent vectors for each vertex via the finite difference method and taking the cross product of the vectors, a correct surface normal is retrieved.
I have a few concerns about my code.
computeVertexNormalsmethod remains untouched, so if this method is called, the normals will be computed from the geometry faces again. The method could be overridden in ParametricGeometry and made to compute normals from the parametric equation, but the overridden method would contain a lot of duplicated code, since the method would still function very similarly. I'm not sure how to proceed.