Some Basics#

[1]:

import os, sys
sys.path.insert(0, os.path.abspath(".."))

import geoclide as gc
import numpy as np

Create a point and a vector#

[2]:

p1 = gc.Point(0., 0., 0.) # create a point
v1 = gc.normalize(gc.Vector(0.5, 0.5, 0.1)) # create a vector and normalize it
p1, v1

[2]:

(Point(0.0, 0.0, 0.0),
 Vector(0.7001400420140049, 0.7001400420140049, 0.140028008402801))

[3]:

v1.length()

[3]:

1.0

Create a ray from the created point and vector#

[4]:

r1 = gc.Ray(o=p1, d=v1)
r1

[4]:

r(t) = (0.0, 0.0, 0.0) + t*(0.7001400420140049, 0.7001400420140049, 0.140028008402801) with t ∈ [0,inf[

[5]:

r1(8)

[5]:

Point(5.601120336112039, 5.601120336112039, 1.120224067222408)

Create a simple triangle mesh composed of 2 triangles#

[6]:

v0 = np.array([-5, -5, 0.])
v1 = np.array([5, -5, 0.])
v2 = np.array([-5, 5, 0.])
v3 = np.array([5, 5, 0.])
vertices = np.array([v0, v1, v2, v3])
f0 = np.array([0, 1, 2]) # the vertices indices of triangle 0 / face 0
f1 = np.array([2, 3, 1]) # the vertices indices of triangle 1 / face 1
faces = np.array([f0, f1])
# We can create a transformation to translate and rotate it
translate = gc.get_translate_tf(gc.Vector(2.5, 0., 0.)) # translation of 2.5 in x axis
rotate = gc.get_rotateY_tf(-90.) # rotation of -90 degrees around the y axis
oTw = translate*rotate # object to world transformation to apply to the triangle mesh
tri_mesh = gc.TriangleMesh(vertices, faces, oTw=oTw) # create the triangle mesh
ds = gc.calc_intersection(tri_mesh, r1) # see if the ray r1 intersect the triangle mesh
ds

[6]:

<xarray.Dataset> Size: 865B
Dimensions:          (xyz: 3, nvertices: 4, ntriangles: 2, p0p1p2: 3, dim_0: 4,
                      dim_1: 4)
Coordinates:
  * xyz              (xyz) int64 24B 0 1 2
Dimensions without coordinates: nvertices, ntriangles, p0p1p2, dim_0, dim_1
Data variables: (12/18)
    o                (xyz) float64 24B 0.0 0.0 0.0
    d                (xyz) float64 24B 0.7001 0.7001 0.14
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B True
    thit             float64 8B 3.571
    ...               ...
    vertices         (nvertices, xyz) float64 96B -5.0 -5.0 0.0 ... 5.0 5.0 0.0
    faces            (ntriangles, p0p1p2) int64 48B 0 1 2 2 3 1
    wTo_m            (dim_0, dim_1) float64 128B 6.123e-17 0.0 1.0 ... 0.0 1.0
    wTo_mInv         (dim_0, dim_1) float64 128B 6.123e-17 0.0 -1.0 ... 0.0 1.0
    oTw_m            (dim_0, dim_1) float64 128B 6.123e-17 0.0 -1.0 ... 0.0 1.0
    oTw_mInv         (dim_0, dim_1) float64 128B 6.123e-17 0.0 1.0 ... 0.0 1.0
Attributes:
    shape:       TriangleMesh
    date:        2025-03-10
    version:     2.0.2
    ntriangles:  2
    nvertices:   4
[7]:

ds['phit']

[7]:

<xarray.DataArray 'phit' (xyz: 3)> Size: 24B
array([2.5, 2.5, 0.5])
Coordinates:
  * xyz      (xyz) int64 24B 0 1 2
Attributes:
    type:         Point
    description:  the x, y and z components of the intersection point