Forums Technical Discussion Expanding or Shrinking a Helix Using Peak

Expanding or Shrinking a Helix Using Peak

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fred_98
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Hi guys,

I guess that if I want to use the peak sop on a helix (that I have no control over the parameters of it) in order to expand it radially then I need to set the normal vectors by using the cross product of the point velocity between two consecutive points and one more cross product between the resulting vector and the velocity vector of one of those two points. Am I right or wrong? If I am right then would you please help me with the vex code for that?
Edited by fred_98 - Feb. 8, 2024 15:54:15
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Enivob
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Just recreate the helix using the helix node. The peak node can only push points so far before uglifying the mesh.
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fred_98
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Sorry for not giving enough details but I am not interested only in the result. I want to learn the process of assigning normal vectors to helical shapes (and other non-uniform curved objects in future).
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N-G
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You can add a PolyFrame node and set the Bitangent parameter to N before your Peak node.
It creates the desired normal vector for your helix.
Edited by N-G - Feb. 8, 2024 18:18:50
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fred_98
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Thanks a lot,
Can I also get the same result using vex(for educational purposes)? please.
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animatrix_
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Here is one way using a Primitive Wrangle:

vector computePerpendicularVector ( vector v )
{
    vector v0 = normalize ( v );
        
    vector y = { 0, 1, 0 };
    vector pv0 = y - ( v0 * dot ( v0, y ) );
    
    vector z = { 0, 0, 1 };
    vector pv1 = z - ( v0 * dot ( v0, z ) );
    
    if ( length2 ( pv0 ) > length2 ( pv1 ) )
        return normalize ( pv0 );
    
    return normalize ( pv1 );
}

int vtxcount = primvertexcount ( 0, @primnum );
if ( vtxcount > 1 )
{
    int pts [ ] = primpoints ( 0, @primnum );
   
    int count = len ( pts );
    
    int isclosed = primintrinsic ( 0, "closed", @primnum );
    if ( pts [ 0 ] != pts [ -1 ] )
    {
        if ( isclosed )
            append ( pts, pts [ 0 ] );
        else
            append ( pts, pts [ -2 ] );
    }
    else
    {
        removeindex ( pts, -1 );
        isclosed = 1;
        count -= 1;
    }
    
    vector tangents [ ] = { };
    vector normals [ ] = { };
    vector bitangents [ ] = { };
    resize ( tangents, count );
    resize ( normals, count );
    resize ( bitangents, count );
    
    for ( int i = 0; i < count; ++i )
    {
        vector p0 = point ( 0, "P", pts [ i ] );
        vector p1 = point ( 0, "P", pts [ i + 1 ] );
        
        vector tangent = normalize ( p1 - p0 );
        if ( isclosed == 0 && i == count - 1 )
            tangent *= -1;
            
        tangents [ i ] = tangent;
    }
    
    vector n = normalize ( cross ( computePerpendicularVector ( tangents [ 0 ] ), tangents [ 0 ] ) );
    normals [ 0 ] = normalize ( cross ( tangents [ 0 ], n ) );
    
    for ( int i = 0; i < count - 1; ++i )
    {
        vector bitangent = cross ( tangents [ i ], tangents [ i + 1 ] );
        if ( length2 ( bitangent ) < 0.0000001 )
            normals [ i + 1 ] = normals [ i ];
        else
        {
            bitangent = normalize ( bitangent );
            float angle = atan2 ( length ( cross ( tangents [ i ], tangents [ i + 1 ] ) ), dot ( tangents [ i ], tangents [ i + 1 ] ) );
            matrix3 rMatrix = ident ( );
            rotate ( rMatrix, angle, bitangent );
            normals [ i + 1 ] = rMatrix * normals [ i ];
        }
        bitangents [ i ] = bitangent;
    }
    
    for ( int i = 0; i < count; ++i )
    {
        if ( chi("normal") )
            setpointattrib ( geoself ( ), chs("n"), pts [ i ], normals [ i ] );
        if ( chi("tangent") )
            setpointattrib ( geoself ( ), chs("t"), pts [ i ], tangents [ i ] );
        if ( chi("bitangent") || ( chi("orient") || chi("rmatrix") ) )
        {
            bitangents [ i ] = normalize ( cross ( normals [ i ], tangents [ i ] ) );
            if ( chi("bitangent") )
                setpointattrib ( geoself ( ), chs("b"), pts [ i ], bitangents [ i ] );
        }
        matrix3 m = 0;
        if ( chi("orient") || chi("rmatrix") )
        {
            m = set ( bitangents [ i ], normals [ i ], tangents [ i ] );
            if ( chi("orient") )
                setpointattrib ( geoself ( ), chs("o"), pts [ i ], quaternion ( m ) );
            if ( chi("rmatrix") )
                setpointattrib ( geoself ( ), chs("rm"), pts [ i ], m );
        }
    }
}

chi parameters are toggles, chs parameters are attribute names.

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