geoclide.quadrics module#

class geoclide.quadrics.Disk(radius, inner_radius=0.0, phi_max=360.0, z_height=0.0, oTw=None, wTo=None)#

Bases: Shape

Creation of the class Disk

Parameters:

radiusfloat: The disk radius
inner_radiusfloat, optional: The inner radius (case of annulus)
phi_maxfloat, optional: The maximum phi value in degrees of the disk/annulus, where phi is between 0 and 360°
z_heightfloat, optional: the disk height along the z axis
oTwTransform, optional: From object to world space or the transformation applied to the spheroid
wToTransform, optional: From world to object space or the in inverse transformation applied to the spheroid

Methods

`area`()	compute the disk / annulus area
`intersect`(r[, ds_output])	Test if a ray/set of rays intersects the disk
`is_intersection`(r)	Test if a ray/set of rays intersects the disk
`is_intersection_t`(r)	Test if a ray/set of rays intersects the disk
`plot`(**kwargs)	Plot the disk
`to_trianglemesh`([reso])	Convert the disk to a triangle mesh

Notes

Even if z_height is given, the origin for rotation transformation do not change. For exemple: z_height=5 then we apply a rotation of 90 degrees around the y axis, the disk we be rotated from (0.,0.,0.), meaning the disk we be moved from position (0.,0.,5.) to (5.,0.,0.).

area()#: compute the disk / annulus area

Warning

the scale transformation is not considered for the area calculation!

intersect(r, ds_output=True)#

Test if a ray/set of rays intersects the disk

Parameters:

rRay: The ray(s) to use for the intersection test(s)
ds_outputBool, optional: If True the output is a dataset, else -> a tuple with intersection information variables

Returns:

outxr.Dataset | tuple: Look-up table with the intersection information if ds_output is True, else returns a tuple. The tuple is ready to be an input for the function geoclide.shapes.get_intersect_dataset

Examples

>>> import geoclide as gc
>>> r1 = gc.Ray(gc.Point(1.2,0.,10.), gc.Vector(0.,0.,-1.))
>>> annulus = gc.Disk(radius=1.5, inner_radius=0.8)
>>> annulus.intersect(r1) # hit point is between the inner radius and radius
<xarray.Dataset> Size: 209B
Dimensions:          (xyz: 3)
Coordinates:
* xyz              (xyz) int64 24B 0 1 2
Data variables:
    o                (xyz) float64 24B 1.2 0.0 10.0
    d                (xyz) float64 24B 0.0 0.0 -1.0
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B True
    thit             float64 8B 10.0
    u                float64 8B 0.0
    v                float64 8B 0.4286
    phit             (xyz) float64 24B 1.2 0.0 0.0
    nhit             (xyz) float64 24B 0.0 0.0 1.0
    dpdu             (xyz) float64 24B 0.0 7.54 0.0
    dpdv             (xyz) float64 24B -0.7 -0.0 -0.0

is_intersection(r)#

Test if a ray/set of rays intersects the disk

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

is_intersectionbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> r1 = gc.Ray(gc.Point(1.2,0.,10.), gc.Vector(0.,0.,-1.))
>>> r2 = gc.Ray(gc.Point(0.2,0.,10.), gc.Vector(0.,0.,-1.))
>>> r3 = gc.Ray(gc.Point(1.6,0.,10.), gc.Vector(0.,0.,-1.))
>>> annulus = gc.Disk(radius=1.5, inner_radius=0.8)
>>> annulus.is_intersection(r1) # hit point is between the inner radius and radius
True
>>> annulus.is_intersection(r2) # the ray passes through the annulus hole, no intersection
False
>>> annulus.is_intersection(r3) # the ray passes outside, no intersection
False

is_intersection_t(r)#

Test if a ray/set of rays intersects the disk

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

thitfloat | 1-D ndarray: The t ray variable(s) for its first intersection at the shape surface
is_intersectionbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> r1 = gc.Ray(gc.Point(1.2,0.,10.), gc.Vector(0.,0.,-1.))
>>> r2 = gc.Ray(gc.Point(0.2,0.,10.), gc.Vector(0.,0.,-1.))
>>> r3 = gc.Ray(gc.Point(1.6,0.,10.), gc.Vector(0.,0.,-1.))
>>> annulus = gc.Disk(radius=1.5, inner_radius=0.8)
>>> annulus.is_intersection_t(r1) # hit point is between the inner radius and radius
(10.0, True)
>>> annulus.is_intersection_t(r2) # the ray passes through the annulus hole, no intersection
(None, False)
>>> annulus.is_intersection_t(r3) # the ray passes outside, no intersection
(None, False)

plot(**kwargs)#

Plot the disk

The disk is first converted to a triangle mesh then the TriangleMesh plot method is used

Parameters:

**kwargs: The keyword arguments are passed on to the TriangleMesh plot method

to_trianglemesh(reso=None)#

Convert the disk to a triangle mesh

Parameters:

resoint, optional: The number of lines around the polar phi angle, minimum accepted value is 3

Returns:

meshTriangleMesh: The disk converted to a triangle mesh

class geoclide.quadrics.Sphere(radius, z_min=None, z_max=None, phi_max=360.0, oTw=None, wTo=None)#

Bases: Shape

Creation of the class Sphere

without transformation the sphere is centered at the origin
z0, z1 and phi_max are needed parameters for the creation of any partial sphere

Parameters:

radiusfloat: The radius of the sphere
z_minfloat, optional: The minimum z value of the sphere where z0 is between [-radius, 0]
z_maxfloat, optional: The maximum z value of the sphere where z1 is between [0, radius]
phi_maxfloat, optional: The maximum phi value in degrees of the sphere, where phi is between 0 and 360°
oTwTransform, optional: From object to world space or the transformation applied to the sphere
wToTransform, optional: From world to object space or the in inverse transformation applied to the sphere

Methods

`area`()	compute the sphere / partial sphere area
`intersect`(r[, ds_output])	Test if a ray/set of rays intersects the sphere/partial sphere
`is_intersection`(r)	Test if a ray/set of rays intersects the sphere / partial sphere
`is_intersection_t`(r)	Test if a ray/set of rays intersects the sphere/partial sphere
`plot`(**kwargs)	Plot the sphere
`to_trianglemesh`([reso_theta, reso_phi])	Convert the sphere to a triangle mesh

area()#: compute the sphere / partial sphere area

Warning

the scale transformation is not considered for the area calculation!

intersect(r, ds_output=True)#

Test if a ray/set of rays intersects the sphere/partial sphere

Parameters:

rRay: The ray(s) to use for the intersection test(s)
ds_outputBool, optional: If True the output is a dataset, else -> a tuple with intersection information variables

Returns:

outxr.Dataset | tuple: Look-up table with the intersection information if ds_output is True, else returns a tuple. The tuple is ready to be an input for the function geoclide.shapes.get_intersect_dataset

Examples

>>> import geoclide as gc
>>> sph1 = gc.Sphere(radius=1.) # sphere of radius 1
>>> sph2 = gc.Sphere(radius=1., z_max=0.5) # partial sphere where portion above z=0.5 is removed
>>> r = gc.Ray(o=gc.Point(-2., 0., 0.8), d=gc.Vector(1.,0.,0.))
>>> sph1.intersect(r)
<xarray.Dataset> Size: 209B
Dimensions:          (xyz: 3)
Coordinates:
* xyz              (xyz) int64 24B 0 1 2
Data variables:
    o                (xyz) float64 24B -2.0 0.0 0.8
    d                (xyz) float64 24B 1.0 0.0 0.0
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B True
    thit             float64 8B 1.4
    u                float64 8B 0.5
    v                float64 8B 0.7952
    phit             (xyz) float64 24B -0.6 0.0 0.8
    nhit             (xyz) float64 24B -0.6 0.0 0.8
    dpdu             (xyz) float64 24B 0.0 -3.77 0.0
    dpdv             (xyz) float64 24B 2.513 0.0 1.885
>>> ds = sph1.intersect(r)
>>> ds['phit'].values # the intersection point
array([-0.6,  0. ,  0.8])
>>> ds['nhit'].values # The surface normal at the intersection point
array([-0.6,  0. ,  0.8])
>>> sph2.intersect(r) # here no intersection since the sphere part above z=0.5 is removed
<xarray.Dataset> Size: 209B
Dimensions:          (xyz: 3)
Coordinates:
* xyz              (xyz) int64 24B 0 1 2
Data variables:
    o                (xyz) float64 24B -2.0 0.0 0.8
    d                (xyz) float64 24B 1.0 0.0 0.0
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B False
    thit             object 8B None
    u                object 8B None
    v                object 8B None
    phit             (xyz) float64 24B nan nan nan
    nhit             (xyz) float64 24B nan nan nan
    dpdu             (xyz) float64 24B nan nan nan
    dpdv             (xyz) float64 24B nan nan nan

is_intersection(r)#

Test if a ray/set of rays intersects the sphere / partial sphere

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

outbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> sph1 = gc.Sphere(radius=1.) # sphere of radius 1
>>> sph2 = gc.Sphere(radius=1., z_max=0.5) # partial sphere where portion above z=0.5 is removed
>>> r = gc.Ray(o=gc.Point(-2., 0., 0.8), d=gc.Vector(1.,0.,0.))
>>> sph1.is_intersection(r)
True
>>> sph2.is_intersection(r) # here no intersection since the sphere part above z=0.5 is removed
False

is_intersection_t(r)#

Test if a ray/set of rays intersects the sphere/partial sphere

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

thitfloat | 1-D ndarray: The t ray variable(s) for its first intersection at the shape surface
is_intersectionbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> sph1 = gc.Sphere(radius=1.) # sphere of radius 1
>>> sph2 = gc.Sphere(radius=1., z_max=0.5) # partial sphere where portion above z=0.5 is removed
>>> r = gc.Ray(o=gc.Point(-2., 0., 0.8), d=gc.Vector(1.,0.,0.))
>>> sph1.is_intersection_t(r)
(1.4000000000000004, True)
>>> sph2.is_intersection(r) # here no intersection since the sphere part above z=0.5 is removed
False

plot(**kwargs)#

Plot the sphere

The sphere is first converted to a triangle mesh then the TriangleMesh plot method is used

Parameters:

**kwargs: The keyword arguments are passed on to the TriangleMesh plot method

to_trianglemesh(reso_theta=None, reso_phi=None)#

Convert the sphere to a triangle mesh

Parameters:

reso_thetaint, optional: The number of lines around the polar theta angle, minimum accepted value is 3
reso_phiint, optional: The number of lines around the azimuth phi angle, minimum accepted value is 3

Returns:

meshTriangleMesh: The sphere converted to a triangle mesh

class geoclide.quadrics.Spheroid(radius_xy, radius_z, oTw=None, wTo=None)#

Bases: Shape

Creation of the class Spheroid

without transformation the spheroid is centered at the origin
spheroid equation: x/(alpha**2) + y/(alpha**2) + z/(gamma**2) = 1, where alpha = radius_xy and gamma = radius_z
prolate -> radius_z > radius_xy
oblate -> radius_z < radius_xy

Parameters:

radius_xyfloat: The equatorial radius of the spheroid
radius_zfloat: The pole radius of the spheroid (distance from center to pole along z axis)
oTwTransform, optional: From object to world space or the transformation applied to the spheroid
wToTransform, optional: From world to object space or the in inverse transformation applied to the spheroid

Methods

`area`()	compute the spheroid area
`intersect`(r[, ds_output])	Test if a ray/set of rays intersects the spheroid
`is_intersection`(r)	Test if a ray/set of rays intersects the spheroid
`is_intersection_t`(r)	Test if a ray/set of rays intersects the spheroid
`plot`(**kwargs)	Plot the spheroid
`to_trianglemesh`([reso_theta, reso_phi])	Convert the spheroid to a triangle mesh

area()#: compute the spheroid area

Warning

the scale transformation is not considered for the area calculation!

intersect(r, ds_output=True)#

Test if a ray/set of rays intersects the spheroid

Parameters:

rRay: The ray(s) to use for the intersection test(s)
ds_outputBool, optional: If True the output is a dataset, else -> a tuple with intersection information variables

Returns:

outxr.Dataset | tuple: Look-up table with the intersection information if ds_output is True, else returns a tuple. The tuple is ready to be an input for the function geoclide.shapes.get_intersect_dataset

Examples

>>> import geoclide as gc
>>> oblate = gc.Spheroid(radius_xy=3., radius_z=1.5)
>>> prolate = gc.Spheroid(radius_xy=1.5, radius_z=3.)
>>> r1 = gc.Ray(o=gc.Point(2.5, 0., 10.), d=(gc.Vector(0., 0., -1.)))
>>> r2 = gc.Ray(o=gc.Point(10., 0., 2.5), d=(gc.Vector(-1., 0., 0.)))
>>> oblate.intersect(r1)
<xarray.Dataset> Size: 209B
Dimensions:          (xyz: 3)
Coordinates:
* xyz              (xyz) int64 24B 0 1 2
Data variables:
    o                (xyz) float64 24B 2.5 0.0 10.0
    d                (xyz) float64 24B 0.0 0.0 -1.0
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B True
    thit             float64 8B 9.171
    u                float64 8B 0.0
    v                float64 8B 0.6864
    phit             (xyz) float64 24B 2.5 0.0 0.8292
    nhit             (xyz) float64 24B 0.6019 -0.0 0.7985
    dpdu             (xyz) float64 24B 0.0 15.71 0.0
    dpdv             (xyz) float64 24B -5.21 0.0 3.927
>>> prolate.intersect(r2)
<xarray.Dataset> Size: 209B
Dimensions:          (xyz: 3)
Coordinates:
* xyz              (xyz) int64 24B 0 1 2
Data variables:
    o                (xyz) float64 24B 10.0 0.0 2.5
    d                (xyz) float64 24B -1.0 0.0 0.0
    mint             int64 8B 0
    maxt             float64 8B inf
    is_intersection  bool 1B True
    thit             float64 8B 9.171
    u                float64 8B 0.0
    v                float64 8B 0.8136
    phit             (xyz) float64 24B 0.8292 0.0 2.5
    nhit             (xyz) float64 24B 0.7985 -0.0 0.6019
    dpdu             (xyz) float64 24B 0.0 5.21 0.0
    dpdv             (xyz) float64 24B -3.927 0.0 5.21

is_intersection(r)#

Test if a ray/set of rays intersects the spheroid

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

outbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> oblate = gc.Spheroid(radius_xy=3., radius_z=1.5)
>>> prolate = gc.Spheroid(radius_xy=1.5, radius_z=3.)
>>> r1 = gc.Ray(o=gc.Point(2.5, 0., 10.), d=(gc.Vector(0., 0., -1.)))
>>> r2 = gc.Ray(o=gc.Point(10., 0., 2.5), d=(gc.Vector(-1., 0., 0.)))
>>> oblate.is_intersection(r1)
True
>>> oblate.is_intersection(r2)
False
>>> prolate.is_intersection(r1)
False
>>> prolate.is_intersection(r2)
True

is_intersection_t(r)#

Test if a ray/set of rays intersects the spheroid

Parameters:

rRay: The ray(s) to use for the intersection test

Returns:

thitfloat | 1-D ndarray: The t ray variable(s) for its first intersection at the shape surface
is_intersectionbool | 1-D ndarray: If there is an intersection -> True, else False

Examples

>>> import geoclide as gc
>>> oblate = gc.Spheroid(radius_xy=3., radius_z=1.5)
>>> prolate = gc.Spheroid(radius_xy=1.5, radius_z=3.)
>>> r1 = gc.Ray(o=gc.Point(2.5, 0., 10.), d=(gc.Vector(0., 0., -1.)))
>>> r2 = gc.Ray(o=gc.Point(10., 0., 2.5), d=(gc.Vector(-1., 0., 0.)))
>>> oblate.is_intersection_t(r1)
(9.170843802411135, True)
>>> oblate.is_intersection_t(r2)
(None, False)
>>> prolate.is_intersection_t(r1)
(None, False)
>>> prolate.is_intersection_t(r2)
(9.170843802411135, True)

plot(**kwargs)#

Plot the spheroid

The spheroid is first converted to a triangle mesh then the TriangleMesh plot method is used

Parameters:

**kwargs: The keyword arguments are passed on to the TriangleMesh plot method

to_trianglemesh(reso_theta=None, reso_phi=None)#

Convert the spheroid to a triangle mesh

Parameters:

reso_thetaint, optional: The number of lines around the polar theta angle, minimum accepted value is 3
reso_phiint, optional: The number of lines around the azimuth phi angle, minimum accepted value is 3

Returns:

meshTriangleMesh: The spheroid converted to a triangle mesh

geoclide.quadrics module#

This Page