slerp: Spherical Linear Interpolation (slerp) on the Unit Sphere
In polarzonoid: Compute Maps and Properties of Polar Zonoids
slerp R Documentation
Spherical Linear Interpolation (slerp) on the Unit Sphere
Description
Let u_0 and u_1 be two unit vectors on the unit sphere \mathbb{S}^{m-1}, that are not antipodal.
The primary purpose of slerp() is to compute uniformly spaced
points along the great circle arc from u_0 to u_1.
The angle step \Delta \theta is computed to be
as large as possible and also satisfy \Delta \theta \le \theta_{max},
where \theta_{max} is a positive user-given parameter.
If the distance between u_0 and u_1 is \theta, then
\Delta \theta = \theta / \text{ceiling}( \theta / \theta_{max}).
The secondary purpose is to compute points on the great circle arc
from user supplied interpolation parameters \tau = a numeric
vector with values typically in [0,1].
The value 0 generates u_0 and 1 generates u_1.
For example to generate n uniformly space points,
set \tau = (0:(n-1))/(n-1) .
Usage
slerp( u0, u1, thetamax=pi/36, tau=NULL )
Arguments
u0, u1
numeric vectors with same length (verified) and unit length (not verified).
If they are antipodal, the great circle arc is undefined and the
function returns NULL.
thetamax
the maximum angular step between successive points on the arc.
This value must be positive.
The default corresponds to 5^\circ.
tau
a numeric vector of interpolation parameters.
The default is NULL which means to ignore it and use thetamax.
If tau is not NULL, then thetamax is ignored.
Details
If both thetamax and tau are not NULL,
tau has priority and thetamax is ignored.
The interpolation formula uses the sin() function.
For details see Shoemake.
Value
slerp() returns an n x m matrix with computed points
in the rows.
n is the number of points, and
m is the length of u0 and u1.
When using thetamax,
n = theta / ceiling(theta/thetamax) + 1,
where theta is the angle between u0 and u1.
Buf if u0 and u1 are equal, then n=1.
When using tau, n=length(tau).
But if tau is empty, the function returns NULL.
In case of error, e.g. u0 and u1 are antipodal,
the function returns NULL.
References
Shoemake, Ken.
Animating Rotation with Quaternion Curves.
pp. 245-254.
SIGGRAPH 1985.
polarzonoid documentation built on June 13, 2025, 9:08 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| slerp | R Documentation |
Spherical Linear Interpolation (slerp) on the Unit Sphere
Description
Let u_0 and u_1 be two unit vectors on the unit sphere \mathbb{S}^{m-1}, that are not antipodal.
The primary purpose of slerp() is to compute uniformly spaced
points along the great circle arc from u_0 to u_1.
The angle step \Delta \theta is computed to be
as large as possible and also satisfy \Delta \theta \le \theta_{max},
where \theta_{max} is a positive user-given parameter.
If the distance between u_0 and u_1 is \theta, then
\Delta \theta = \theta / \text{ceiling}( \theta / \theta_{max}).
The secondary purpose is to compute points on the great circle arc
from user supplied interpolation parameters \tau = a numeric
vector with values typically in [0,1].
The value 0 generates u_0 and 1 generates u_1.
For example to generate n uniformly space points,
set \tau = (0:(n-1))/(n-1) .
Usage
slerp( u0, u1, thetamax=pi/36, tau=NULL )
Arguments
u0, u1 |
numeric vectors with same length (verified) and unit length (not verified).
If they are antipodal, the great circle arc is undefined and the
function returns |
thetamax |
the maximum angular step between successive points on the arc.
This value must be positive.
The default corresponds to 5 |
tau |
a numeric vector of interpolation parameters.
The default is |
Details
If both thetamax and tau are not NULL,
tau has priority and thetamax is ignored.
The interpolation formula uses the sin() function.
For details see Shoemake.
Value
slerp() returns an n x m matrix with computed points
in the rows.
n is the number of points, and
m is the length of u0 and u1.
When using thetamax,
n = theta / ceiling(theta/thetamax) + 1,
where theta is the angle between u0 and u1.
Buf if u0 and u1 are equal, then n=1.
When using tau, n=length(tau).
But if tau is empty, the function returns NULL.
In case of error, e.g. u0 and u1 are antipodal,
the function returns NULL.
References
Shoemake, Ken. Animating Rotation with Quaternion Curves. pp. 245-254. SIGGRAPH 1985.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.