서지주요정보
General schemes for unit quaternion curve construction = 단위 쿼터니언 곡선의 일반적인 생성법
서명 / 저자 General schemes for unit quaternion curve construction = 단위 쿼터니언 곡선의 일반적인 생성법 / Myoung-Jun Kim.
저자명 Kim, Myoung-Jun ; 김명준
발행사항 [대전 : 한국과학기술원, 1996].
Online Access 원문보기 원문인쇄

소장정보

등록번호

8006392

소장위치/청구기호

학술문화관(문화관) 보존서고

DCS 96016

휴대폰 전송

도서상태

이용가능

대출가능

반납예정일

등록번호

9002242

소장위치/청구기호

서울 학위논문 서가

DCS 96016 c. 2

휴대폰 전송

도서상태

이용가능

대출가능

반납예정일

초록정보

This thesis proposes a new class of unit quaternion curves in the orientation space SO(3), which is a fundamental tool for computer animation involving solid rotations or orientations. We develop a method to transform a curve defined as a weighted sum of basis functions into its unit quaternion analogue. Applying the method to well-known curves including $B\acute{e}zier$, Hermite and B-spline curves, we are able to construct various unit quaternion curves which share nice properties such as continuity and local control property with their original curves. Each of the resulting curves is defined in a closed form, and their expressions are so simple that they are easy to be evaluated and differentiated. We first give a $B\acute{e}zier$ unit quaternion curve with n-control points. Then, the cubic $B\acute{e}zier$ quaternion curve is extended to a Hermite unit quaternion curve, which matches given orientations and angular velocities at its ends. Unlike the previous Hermite unit quaternion curves, it is possible to specify arbitrary angular velocities at the curve ends. From experiments, we show that our Hermite unit quaternion curves use less torque than the previous ones. We also give a B-spline unit quaternion curves defined in closed forms and verify that our B-spline unit quaternion curve of order k is $C^{k-2}$-continuous and locally controllable. Since the B-spline unit quaternion curve does not interpolate its control points as the usual B-spline curves in $R^3$, we provide a method to find the control points which makes the B-spline quaternion curve interpolating a given sequence of unit quaternions. The ease of differentiation of our unit quaternion curves makes it possible to do extensive analyses on the curves. We present the formulas for computing high order derivatives of angular velocity of a $B\acute{e}zier$ quaternion curve at the curve ends. By solving the formulas for its control points, we are able to construct a $C^k$-continuous Hermite quaternion curve interpolating a given sequence of differential end conditions. The differentiation of quaternion curves is used to estimate the error of quaternion approximation. We give a bound on the error of the Hermite quaternion approximation, where piecewise cubic Hermite quaternion curves are used to approximate a given quaternion curve.

서지기타정보

서지기타정보
청구기호 {DCS 96016
형태사항 [iii], 99 p. : 삽도 ; 26 cm
언어 영어
일반주기 저자명의 한글표기 : 김명준
지도교수의 영문표기 : Sung-Yong Shin
지도교수의 한글표기 : 신성용
학위논문 학위논문(박사) - 한국과학기술원 : 전산학과,
서지주기 Reference : p. 97-99
주제 Quaternion
Spline
Interpolation
Rotation
SO(3)
쿼터니언
스플라인
보간
회전
회전그룹
QR CODE qr code