squared_distance_to_element

`squared_distance_to_element(point, V, element)`

Squared distance from a point to a mesh element (point, edge, triangle)

Parameters:

Name Type Description Default
`point` `(dim,) numpy double array`

Query point coordinates

required
`V` `(v,dim) numpy double array`

Matrix of mesh/polyline/pointcloud vertex coordinates

required
`element` `(s,) numpy int array`

Vector of element indices into V

required

Returns:

Name Type Description
`sqrD` `double`

Squared minimum distance from point to mesh element

squared_distance.

Examples:

``````# Generate random mesh
V = np.random.rand(3,3)
F = np.array([0,1,2],dtype=int)
# Generate random query point
P = np.random.rand(3)
# Calculate distance from point to triangle
sqrD = gpytoolbox.squared_distance_to_element(P,V,F)
``````
Source code in `src/gpytoolbox/squared_distance_to_element.py`
 ``` 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77``` ``````def squared_distance_to_element(point,V,element): """Squared distance from a point to a mesh element (point, edge, triangle) Parameters ---------- point : (dim,) numpy double array Query point coordinates V : (v,dim) numpy double array Matrix of mesh/polyline/pointcloud vertex coordinates element : (s,) numpy int array Vector of element indices into V Returns ------- sqrD : double Squared minimum distance from point to mesh element See Also -------- squared_distance. Examples -------- ```python # Generate random mesh V = np.random.rand(3,3) F = np.array([0,1,2],dtype=int) # Generate random query point P = np.random.rand(3) # Calculate distance from point to triangle sqrD = gpytoolbox.squared_distance_to_element(P,V,F) ``` """ dim = V.shape[1] if element.ndim>1: element = np.ravel(element) simplex_size = element.shape[0] if simplex_size==1: # Then this is just distance between two points sqrD = np.sum((V[element] - point)**2.0) lmb = 1 elif simplex_size==2: if dim==2: V = np.hstack(( V,np.zeros((V.shape[0],1)) )) point = np.concatenate((point,np.array([0]))) # Distance from point to segment start = V[element[0],:] end = V[element[1],:] line_vec = end - start pnt_vec = point - start line_len = np.linalg.norm(line_vec) line_unitvec = line_vec/line_len pnt_vec_scaled = pnt_vec/line_len t = np.dot(line_unitvec, pnt_vec_scaled) if t < 0.0: t = 0.0 elif t > 1.0: t = 1.0 nearest = t*line_vec sqrD = np.sum((nearest - pnt_vec)**2.0) nearest = start + nearest lmb = [1-t,t] elif simplex_size==3: assert(dim==3) sqrD = 0 tri = np.vstack(( V[element[0],:], V[element[1],:], V[element[2],:] )) # print(tri) sqrD,nearest_point = pointTriangleDistance(tri,point) lmb = barycentric_coordinates(nearest_point,V[element[0],:],V[element[1],:],V[element[2],:]) return sqrD,lmb ``````