/**
* Copyright (c) 2013 Oculus Info Inc.
* http://www.oculusinfo.com/
*
* Released under the MIT License.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
* of the Software, and to permit persons to whom the Software is furnished to do
* so, subject to the following conditions:
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package spimedb.util.geom.cartesian;
/**
* A fourth-order spline that allows fitting of points and velocities, and
* matching of acceleration, at join points.
*
* The general formula for the spline is a basic parameterized fourth-order
* polynomial, by segment (s):
* x_s_n(t) = a_s_n t^4 + b_s_n t^3 + c_s_n t^2 + d_s_n t + e_s_n
* x'_s_n(t) = 4 a_s_n t^3 + 3 b_s_n t^2 + 2 c_s_n t + d_s_n
* x"_s_n(t) = 12 a_s_n t^2 + 6 b_s_n t + 2 c_s_n
*
* We are trying to match:
* x_s_n(0) = p0_s_n X_s(0) is the first point of segment s
* x'_s_n(0) = v0_s_n X'_s(0) is the velocity at the first point of the segment s
* x_s_n(1) = p1_s_n X_s(1) is the last point of the segment s
* x'_s_n(1) = v1_s_n X'_s(1) is the velocity at the last point of the segment s
* p1_s_n = p0_s+1_n The last point of segment s matches the first point of segment s+1
* v1_s_n = v0_s+1_n The velocity at the last point of segment s matches the velocity at the first point of segment s+1
* x"_s_n(1) = x"_s+1_n(0) The acceleration at the last point of segment s matches the acceleration at the first point of segment s+1
*
* This give us our 5 unknowns
*
* e_s_n = p0_s_n
* d_s_n = v0_s_n
*
*
* @author Nathan
*/
public class QuarticSpline {
}