• Journal of Computational Design and Engineering
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• 제2권1호
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• pp.1-15
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• 2015

Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically performs approximate B-spline volume lofting, which decomposes the problem into three sub-problems of multiple B-spline curve fitting along u-, v-, and w-parametric directions. Especially, it makes the efficient use of knots in the multiple B-spline curve fitting and thereby accomplishes adaptive knot placement along each parametric direction of a resulting B-spline volume. The proposed method is quite useful to realize efficient data reduction while smoothing out the noises and keeping the overall features of BRDF data well. By applying the B-spline volume models of real materials for rendering, we show that the B-spline volume models are effective in preserving the features of material appearance and are suitable for representing BRDF data.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• 제5권1호
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• pp.40-45
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• 2002

The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

• 한국CDE학회논문집
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• 제13권6호
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• pp.469-477
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• 2008

Physically-based rendering is an image synthesis technique based on simulation of physical interactions between light and surface materials. Since generated images are highly photorealistic, physically-based rendering has become an indispensable tool in advanced design visualization for manufacturing and architecture as well as in film VFX and animations. Especially, BRDF (bidirectional reflectance distribution function) is critical in realistic visualization of materials since it models how an incoming light is reflected on the surface in terms of intensity and outgoing angles. In this paper, we introduce techniques to represent BRDF as B-spline volumes and to utilize them in physically-based rendering. We show that B-spline volume BRDF (BVB) representation is suitable for measured BRDFs due to its compact size without quality loss in rendering. Moreover, various CAGD techniques can be applied to B-spline volume BRDFs for further controls such as refinement and blending.

• 대한기계학회논문집A
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• 제40권4호
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• pp.373-379
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• 2016

복잡한 불균질성을 가지는 뼈의 경우 물성치 분포를 B-스플라인 볼륨 함수를 이용해 표현하는 것이 적합하다고 알려져 있다. 물성치 분포에 대한 B-스플라인 볼륨 함수는 CT 영상의 각 화소값들을 보간하여 얻을 수 있다. 그러나 뼈의 CT 영상 데이터는 3차원이며 크기가 매우 크기 때문에 보간 시간이 오래 걸리며, 많은 컴퓨터 메모리가 필요하다. 본 연구에서는 이를 해결하기 위한 방법을 제안한다. 제안하는 방법에서는 영상이 가지는 화소 간격의 균일성 및 B-스플라인 기저 함수의 특징을 이용해 B-스플라인 볼륨 보간 문제를 단순화 시킨다. 이는 결과적으로 계산 시간 및 메모리 사용량을 줄여준다. 검증을 위해, 제안한 방법을 컴퓨터 프로그램으로 구현하였으며, 실험을 통해 계산 시간이 줄어든 것을 확인하였다.

• 한국측량학회:학술대회논문집
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• 한국측량학회 2002년도 창립 20주년기념 국제학술대회
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• pp.229-238
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• 2002

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to improve the accuracy of earthwork calculation. In this paper, we propose an algorithm of finding a cubic spline surface with the free boundary conditions, which interpolates the given three dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors especially concerned with accuracy of volume computations. We present some computational results showing that our proposed method provides good accuracy.

• Korean Journal of Geomatics
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• 제2권1호
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• pp.25-29
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• 2002

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to improve the accuracy of earthwork calculation. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors especially concerned with accuracy of volume computations. We present some computational results showing that our proposed method provides good accuracy.

• 한국CDE학회논문집
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• 제3권2호
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• pp.87-102
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• 1998

Given a sequence of cross-sectional curves, the skinning method generates a freeform surface that interpolates the given curves in that sequence. This thesis presents a construction method of a B-spline skinning surface that is fair and satisfies volume constraints. The fairness metric is based on the parametric energy functional of a surface. The degrees of freedom in surface control are closely related lo control points in the skinning direction. The algorithm fur finding a skinning surface consists of two step. In the first step, an initial fair surface is generated without volume constraints and one coordinate of each control point is fixed. In the second step, a final surface that meets all constraints is constucted by rearranging the other coordinates of each control point that defines the initial surface A variational Lagrange optimization method produces a system of nonlinear equations, which can be solved numerically. Moreover, the reparametrization of given sectional curves is important for the construction of a reasonable skinning surface. This thesis also presents an intuitive metric for reparametrization and gives some examples that are optimized with respect to that metric.

• 한국CDE학회논문집
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• 제2권1호
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• pp.11-18
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• 1997

Scientific volume visualization addresses the representation, manipulation, and rendering of volumetric data sets, providing mechanisms for looking closely into structures and understanding their complexity and dynamics. In the past several years, a tremendous amount of research and development has been directed toward algorithms and data modeling methods for a scientific data visualization. But there has been very little work on developing a mathematical volume model that feeds this visualization. Especially, in flow visualization, the volume model has long been required as a guidance to display the very large amounts of data resulting from numerical simulations. In this paper, we focus on the mathematical representation of volumetric data sets and the method of extracting meaningful information from the derived volume model. For this purpose, a B-spline volume is extended to a high dimensional trivariate model which is called as a flow visualization model in this paper. Two three-dimensional examples are presented to demonstrate the capabilities of this model.

• 한국컴퓨터그래픽스학회논문지
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• 제22권3호
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• pp.1-9
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• 2016

볼륨 가시화의 샘플링 단계에서는 보통 선형 보간이 사용된다. 선형 보간은 일반적으로 좋은 화질의 영상을 생성하지만 의료영상 소프트웨어는 높은 화질의 영상이 필요하기 때문에 경우에 따라 높은 기대에 미치지 못한다. 본 연구는 샘플링 단계에서 B 스플라인을 기반으로 하는 삼차 보간을 수행한다. 기존의 B 스플라인은 제어점을 지나지 않는 근사 함수이므로, 본 연구는 제어점을 이동하여 생성된 곡선이 원래의 제어점을 지나도록 하였다. 가시화 단계에서는 속도를 향상하기 위해 빈공간 도약을 적용 가능하다. 빈공간을 파악하기 위해서는 각 블록에 대한 최대값과 최소값을 계산해야 한다. B 스플라인은 볼록포 성질이 있어서, 제어점의 값을 최대값과 최소값으로 사용할 수 있다. 그 결과로 삼차 보간 기반의 볼륨 가시화가 대화적 속도로 가능하다.

• 한국해양공학회지
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• 제16권4호
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• pp.19-24
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• 2002

항만공사같은 대규모의 매립공사에서 토공작업은 총공사비의 상당한 비중을 차지하므로 경제적인 시공을 위하여 절.성토량은 정확하게 계산되어야 한다. 따라서 본 연구는 주어진 3차원 표고데이터를 지나는 스플라인 곡면을 구하는 알고리즘을 제시함으로써 좀더 정확한 토공량 계산식의 결정을 목표로 한다. 스플라인에 대한 흥미로운 수학적 결과는 무척 많지만 본 연구에서는 스플라인 곡면을 기술하고 또, 그것을 이용하여 토공량 계산을 위한 알고리즘개발을 목표로 하기 때문에 알고리즘과 프로그래밍에 필요한 수학적 내용을 기술하며 그 수치적 계산결과는 Maple 프로그램을 이용하였다. 그리고 정확도를 비교하기 위하여 기존의 방법인 선형점고법, Chamber법, Chen과 Lin의 이론을 컴퓨터프로그램하여 본 연구에서 제시된 방법과 정확도를 비교, 분석한다. 아울러 각 이론식의 결과에 대한 보다 정확한 검사를 위하여 x, y 함수식을 이용한 실험지형을 인위적으로 만들었으며 그 때의 값을 기준값으로 하였다. 따라서 실험수치지형에 대한 기준값이 절대값에 가까우므로 각 토공량식들의 오차규명을 보다 명확하고 확실하게 비교할 수 있도록 하였다.