DeCasteljau

Constructs a quaternions spline using the De Casteljau
 algorithm.

Provides routines to create some quaternions splines:
Barry-Goldman algorithm, De Casteljau algorithm, and Kochanek-Bartels
algorithm. The implementations are based on the Python library
'splines'. Quaternions splines allow to construct spherical curves.
References: Barry and Goldman <doi:10.1145/54852.378511>,
Kochanek and Bartels <doi:10.1145/800031.808575>.

Stc3<a9>phane Laurent

qsplines

Quaternions Splines

Stéphane Laurent

Matthias Geier

DeCasteljau function

<dl><dt>segments</dt>
<dd>a list of vectors of unit quaternions; each segment must
contain at least two quaternions</dd>
<dt>keyTimes</dt>
<dd>the times corresponding to the segment boundaries, an
increasing vector of length <code>length(segments)+1</code>; if <code>NULL</code>,
it is set to <code>1, 2, ..., length(segments)+1</code></dd>
<dt>n_intertimes</dt>
<dd>a positive integer used to linearly interpolate the 
times given in <code>keyTimes</code> in order that there are
<code>n_intertimes - 1</code> between two key times (so one gets the key
times if <code>n_intertimes = 1</code>); this parameter must be given if 
<code>constantSpeed=TRUE</code> and if it is given when 
<code>constantSpeed=FALSE</code>, then it has precedence over <code>times</code></dd>
<dt>times</dt>
<dd>the interpolating times, they must lie within the range of
<code>keyTimes</code>; ignored if <code>constantSpeed=TRUE</code> or if 
<code>n_intertimes</code> is given</dd>
<dt>constantSpeed</dt>
<dd>Boolean, whether to re-parameterize the spline to
have constant speed; in this case, <code>"times"</code> is ignored and a
function is returned, with an attribute <code>"times"</code>, the vector of
new times corresponding to the key rotors</dd></dl>

Arguments

Spline using the De Casteljau algorithm — DeCasteljau

<dl>

<dt>segments</dt>
<dd>a list of vectors of unit quaternions; each segment must
contain at least two quaternions</dd>


<dt>keyTimes</dt>
<dd>the times corresponding to the segment boundaries, an
increasing vector of length <code>length(segments)+1</code>; if <code>NULL</code>,
it is set to <code>1, 2, ..., length(segments)+1</code></dd>


<dt>n_intertimes</dt>
<dd>a positive integer used to linearly interpolate the 
times given in <code>keyTimes</code> in order that there are
<code>n_intertimes - 1</code> between two key times (so one gets the key
times if <code>n_intertimes = 1</code>); this parameter must be given if 
<code>constantSpeed=TRUE</code> and if it is given when 
<code>constantSpeed=FALSE</code>, then it has precedence over <code>times</code></dd>


<dt>times</dt>
<dd>the interpolating times, they must lie within the range of
<code>keyTimes</code>; ignored if <code>constantSpeed=TRUE</code> or if 
<code>n_intertimes</code> is given</dd>


<dt>constantSpeed</dt>
<dd>Boolean, whether to re-parameterize the spline to
have constant speed; in this case, <code>"times"</code> is ignored and a
function is returned, with an attribute <code>"times"</code>, the vector of
new times corresponding to the key rotors</dd>

</dl>

DeCasteljau: Spline using the De Casteljau algorithm

Description

Usage

Value

Arguments