• Title, Summary, Keyword: offset curve

### An offset algorithm with forward tracing of tangential circle for open and closed poly-line segment sequence curve (접원의 전방향 경로이동에 의한 오프셋 알고리즘)

• Yun, Seong-Yong;Kim, Il-Hwan
• Proceedings of the KIEE Conference
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• pp.1022-1030
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• 2003
• In this paper we propose a efficient offset curve construction algorithm for $C^0$-continuous Open and Closed 2D sequence curve with line segment in the plane. One of the most difficult problems of offset construction is the loop problem caused by the interference of offset curve segments. Prior work[1-10] eliminates the formation of local self-intersection loop before constructing a intermediate(or raw) offset curve, whereas the global self-intersection loop are detected and removed explicitly(such as a sweep algorithm[13]) after constructing a intermediate offset curve. we propose an algorithm which removes global as well as local intersection loop without making a intermediate offset curve by forward tracing of tangential circle. Offset of both open and closed poly-line segment sequence curve in the plane constructs using the proposed approach.

### EXPLICIT ERROR BOUND FOR QUADRATIC SPLINE APPROXIMATION OF CUBIC SPLINE

• Kim, Yeon-Soo;Ahn, Young-Joon
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009
• In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

### HAUSDORFF DISTANCE BETWEEN THE OFFSET CURVE OF QUADRATIC BEZIER CURVE AND ITS QUADRATIC APPROXIMATION

• Ahn, Young-Joon
• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007
• In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

### An offset Curve Generation Method for the Computer Pattern Sewing Machine (컴퓨터 패턴 재봉기에서의 오프셋 곡선 생성 방법)

• Oh, Tae-Seok;Yun, Sung-Yong;Kim, Il-Hwan
• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.188-196
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• 2007
• In this paper we propose an efficient offset curve generation algorithm for open and closed 2D point sequence curve(PS curve) with line segments in the plane. One of the most difficult problems of offset generation is the loop intersection problem caused by the interference of offset curve segments. We propose an algorithm which removes global as well as local intersection loop without making an intermediate offset curve by forward tracing of tangential circle. Experiment in computer sewing machine shows that proposed method is very useful and simple.

### Computing Planar Curve Offset Based on Surface/Surface Intersection (교차곡선 연산을 이용한 평면 곡선의 오프셋 계산)

• 최정주
• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998
• This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

### A Tessellation of a Planar Polynomial Curve and Its Offset (평면곡선과 오프셋곡선의 점열화)

• Ju, S.Y.;Chu, H.
• Korean Journal of Computational Design and Engineering
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• v.9 no.2
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• pp.158-163
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• 2004
• Curve tessellation, which generates a sequence of points from a curve, is very important for curve rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal deviation. Our approach has two merits. One is that it guarantees satisfaction of a given tolerance, and the other is that it can be applied in not only a polynomial curve but its offset. Especially the point sequence generated from an original curve can cause over-cutting in NC machining. This problem can be solved by using the point sequence generated from the offset curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.

### GEOMETRIC CONIC SPLINE APPROXIMATION IN CAGD

• Ahn, Young-Joon
• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002
• We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

### Evaluation by modified offset method on J-R curve with negative crack growth (부균열을 가진 J-R곡선의 수정옾셋방법에 의한 평가)

• 안광주;최재강
• Journal of the Korean Society of Safety
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• v.12 no.3
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• pp.45-51
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• 1997
• To evaluate the elastic-plastic fracture toughness by this modified offset method, the origin of J-R curve is set with drawing the blunting line on the maximum point of the negative crack growth and R curve is modified by adding the blunting factor of the experimented point on the R curve. The elastic-plastic fracture toughness $J_{IC]$ of A5083-H112 material by the modified offset method we 44kN/m on the smooth CT specimens.

### Comparison of Offset Approximation Methods of Conics with Explicit Error Bounds

• Bae, Sung Chul;Ahn, Young Joon
• Journal of the Chosun Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016
• In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

### Shape offectting using the geometric properties of B -spline curve(1) -A Study on offsetting of B-spline control polygon- (B-스플라인 곡선의 기하특성을 이용한 형상 옵셋(1) -B-스플라인 제어 다각형 옵셋 기법의 연구-)

• 정재현;김희중
• Journal of the Korean Society of Marine Engineering
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• v.20 no.1
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• pp.44-48
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• 1996
• In manufacturing of exact products, the offsetting is required to transfer the design data of shape to manufacturing data. In offsetting the degeneracies are occurred, and these problems are mere difficult in freeform shapr manufacuring. This paper is using the geometric properties of B-spline curves to solve the degeneracy of offsetting and to generating of enhanced offsetting. The offsetting of B-spline control polygon spans generates exact control polygon of original shapes. This method is faster in generating offset curve than the normal offsetting, and the resulted offset curves are exact. The additional property of this method is using to control offset shape as B-spline curves. We believe that this method is as effective solution for modifying of offset curves.