A contribution to curves network based ship hull form reverse engineering

Abstract

In reverse engineering (RE) there are several strategies, technologies and mathematical numerics involved from data acquisition system to surface fitting. This makes the reverse engineering methods always computationally expensive, time taking and more over error prone. Therefore, developing application specific RE method can offer the required quality with reasonable associated time and then cost. This paper presents a practical and efficient ship hull form reconstruction strategy which align the reverse engineering results into traditional hull form design procedures. The developed approach reads points from a set of unorganized noisy 3D point cloud and fits to cross-sectional curves network (transversal and waterline sections). It consists of several point cloud pre-processing functions, the curves fitting (interpolation and approximation) and presents different Non-Uniform Rational B-Spline (NURBS) surface fitting approaches from curves network. The point cloud pre-processing removes outliers and extracts transversal and waterline sections. It is also equipped with different functions to successfully filter and smooth point cloud so that it can be fitted to curves by interpolation or approximation. The suitability of different existing surface generations (lofting, patching and surface from curves network) are experimented based on cross-sectional curves. The developed approach is tested against two hull forms (scanned and manually generated) point cloud. The tests reveals that, the developed approach is time saving and suitable for hull form reconstruction.

Keywords

Reverse engineering hull form point cloud curves network surface fitting

1. Introduction

Reverse engineering (RE) in the context of Computer Aided Design (CAD) is an activity which deals with digitization of a real objects in order to create a numerical or virtual model [33]. RE in CAD systems with regard to product development has received extensive focus with the development of laser scanner technology and other data acquisition systems. Nowadays, companies, organization and suppliers need to construct CAD models from physical objects for retrofit and/or redesign purposes. Therefore, RE becomes a very important element to reconstruct physical models where the documentation about the components may be unavailable, incomplete or in a form incompatible with the modern CAD and manufacturing software. The economic crisis over the last few years increases the importance of RE in maritime industries. Due to economic and environmental constraints and a decrement in freight rates, maritime companies have to change the operation conditions of their vessels. To sail/work competitive in the new economic environment, the maritime system has to be overhauled to meet the new tasks [15]. The production and design data is needed for the analyses and reconstruction, but in most cases it is not available as it is generally not part of the documentation. Therefore RE methods are an important solution for retrofitting and redesign purposes to recreate the product model of maritime structures.

2. Related works

The use of CAD, computational analysis and optimization in any industries with regard to complex high-performance products is inevitable. For rapid product development two technologies (i.e. RE and rapid prototyping) have received extensive attention recently from both research and industrial areas. In particular, RE is an important method for reconstructing the CAD model from a physical object that already exists [3,18]. The process starts from digitizing the existing objects, i.e., capturing a point cloud data of the part surface with digitizers or coordinate measuring devices. The measured points are then transformed into a CAD model using approximation or interpolation techniques [54]. Mathematical attempts to reconstruct surfaces from point clouds was published a long time ago [14], several surface reconstruction techniques have been proposed over the last decades. In recent years, laser scanning technology has developed rapidly and has become a powerful tool in acquiring the point cloud data of large and complex object models [54]. Therefore research communities have paid special attention to develop efficient and robust surface reconstruction algorithm and some software such as 3D Reshaper, Geomagic, PolyWorks and etc. claim to do so. Although various reconstruction methods have been proposed [2,13,16,19,25,27,35,53], many problems still remain to be addressed due to geometric complexity of the shapes and noise or outliers in measured data, to the contrary high accuracy reconstruction requirements and newly arisen applications [26]. There exists an extensive literature, which addresses different questions of surface reconstruction. The problem starts from point cloud data acquisition systems (calibration, accuracy, placement and multiple views), kind of physical object (occlusion, surface finish, accessibility) and the nature of data (extremely disorganized, noisy and incomplete). The data obtained through all these procedures are the main source of information in the 3D surface reconstruction and not suitable to integrate into the CAD systems [12,24].

Several strategies to reconstruct CAD models from point cloud have been published [22,23,37,38,46,48,49,51], but it is not trivial as surface fitting is a highly non-linear problem as the ideal number of control points to be searched in unknown dimensionality, the knot vectors, and the parameters values of the data points, and the ideal weights of the smoothness functional are unknown. Many research efforts have been paid to figure out effective, robust, time saving and accurate reconstruction strategies for the specific or general applications. But there is no straightforward recipe how to proceed to obtain a good quality of surface when it comes to complex surfaces.

In RE the most employed reconstruction method is 3D triangulation of the point cloud. This approach seems to be slow as the number of data points gets larger and larger and might have limitations when it comes to concave parts and hole loops within a point cloud [19,21,25,26,35,49]. Furthermore surface fitting based on triangular surface is computationally expensive in terms of computer memory and processing time as it includes complicated procedures of refinement, parametrization and maintainability of the continuity between networks of patches. Noting the above limitations, an alternative direct surface fitting to point cloud [12,23,37,38,48] and cross sectional curves network methods [5,8,50] are proposed. Direct surface fitting has a difficulty to be applied over occlude surfaces [22].

Attempts have been made to develop methods to reconstruct maritime structures from point cloud data [11,20,29–32,39]. However, effective and robust procedures are not in place because of RE related complexity and insufficient maritime specific studies. It is also partially because of the difference in traditional RE design processes and strategies with other industries (e.g. automotive, robotics and etc.) where considerable RE practices are well developed.

Therefore the development of reconstruction method for specific application improves the quality as it enables to specifically adjust the algorithm based on the shape and features of specific object. This paper presents, a RE method for specific object (ship hull form) based on curves network surface fitting. The proposed system has the following advantages compared to traditional RE methods:

avoid the need to compute the local properties (e.g. surface normal and curvature) based on point cloud which are always computationally expensive and error prone;

decrease the large number of input points to manageable size very quickly;

avoid the 3D triangulation based on point cloud which is computationally expensive in terms of computer memory and processing time as it includes complicated procedures of refinement and parametrization;

provides semi-automatic curves (transversal and waterline sections curves) fitting to point cloud;

NURBS surface fitting based on transversal section and waterline curves is well developed and it fits the hull form RE into the traditional hull form design procedure.

3. The developed reverse engineering methodology

In RE there are several strategies, technologies and mathematical numerics involved from data acquisition system to surface fitting. This makes the RE methods computationally expensive, time taking and more over error prone. Therefore, developing or selecting the best measurement approach and reconstruction methods (such as following specific pre-processing of point cloud, parametrization, curves and surfaces fitting including the post-processing methods such as fairing) can offer the required quality with reasonable associated cost and time. This work exclusively presents, the semi-automatic cross sectional RE system for ship hull form. The developed methodology broadly consists of three parts (point data pre-processing, cross-sectional curves fitting and surface generation) as shown in Fig. 1.

Fig. 1.

The general layout of the developed methodology. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

The point data pre-processing is developed based on Point Cloud library (PCL) and additional own codes. PCL is a standalone, large scale, open project for images and point cloud processing [41]. The cross-sectional curves interpolation and approximation after point data pre-processing are developed based on a software development platform (Open CASCADE Technology) library which includes many C++ components for 3D surface and solid modeling, visualization, data exchange and rapid application development [36]. Using the mentioned libraries a semi-automatic tool which fits transversal and waterline section curves to registered point cloud is developed. The developed framework provides the interpolated and/or approximated curves in Initial Graphics exchange Specification (IGES). Then the NURBS surfaces can be generated from curves network using well-developed traditional procedures. The developed methodology reads point cloud data from $x y z$ -coordinates (*.txt), Point Cloud Data (*.pcd) and Polygon File Format (*.ply). The developed system and its components will be explained step by step in the following sections.

3.1. Point data pre-processing

3D digitization most often results in numerous unwanted points. These points frequently belong to objects which surround the object being digitized, such as fixtures, measurement area or some other part of the assembly to which the digitized part belongs. However, in the case of non-contact methods, such as the laser triangulation, those points can originate from objects located further away. To some extent, the unwanted points can also be the result of measurement errors (due to operator errors, system-specific errors and/or errors due to specific nature of the digitized object, some external disturbance i.e., vibrations), etc. Those points, have to be eliminated in order to maintain the quality of the surface reconstruction. The point cloud pre-processing is developed to allow elimination of unwanted points. The pre-processing of point cloud towards curves network method ship hull form reconstruction consists of three modules: outliers removal, cross-sectional point data extraction, cross-sectional filtering and smoothing of point data.

3.1.1. Outliers removal

This module removes unwanted point cloud such as Not a Number (NaN) and outliers imported with the input file. Outliers detection in point clouds is not a trivial task since there are: geometrical discontinuities caused by occlusions in silhouette boundaries, no prior knowledge of the statistical distribution of points, the existence of noise and different local point densities [47]. In this work different outliers removal strategies are investigated to eliminate the outliers exist in a noisy sets of points as shown in Fig. 2(a). Four robust methods are implemented for this specific application: bounding domain, conditional outliers removal, radius neighborhood and statistical methods.

Fig. 2.

The outliers removal methods, (a) the general algorithm layout implemented to remove the outliers in the point cloud, (b) shows the working principle of radius neighborhood outliers removal method, (c) shows the normal Gaussian distribution with different number of standard deviation tolerance coefficients used in statistical outliers removal. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Bounding domain method. This is the simplest and rough outliers filtering method next to NaN removal. The user defines the maximum and minimum 3D coordinates of bounding domain. Hence the algorithm deletes all point sets outside the bounding domain. It is used to remove extreme outliers points originally not belong to the target object but the fixtures, and the surrounding objects or extreme reflections.

Conditional outliers removal method. Conditional filtering method removes all indices in the given input cloud that do not satisfy one or more given conditions. This method helps to retrieve some interest area by setting certain condition which the given point must satisfy for it to remain in the required point cloud. Comparisons in 3D space are implemented to retrieve the interest area, for instance, one can retrieve the bow or stern region of the hull form using comparison conditions.

Radius neighborhood method. It iterates through the entire input points and determines the number of neighboring points based on the defined radius of the sphere. The points with too few neighbors will be considered as outliers. Figure 2(b) demonstrates the radius outliers removal method, with two user defined variables (the radius of the sphere and the number of neighboring points which define whether the points are outliers or not). In the figure, the radius $r_{1}$ is greater than $r_{2}$ , and with the radius $r_{1}$ set and the number of neighboring points set to 1, then only the point inside the sphere ( $r_{1}$ ) will be considered as outliers. With radius set to $r_{2}$ and the number of allowed neighboring points are 2, then all the points in all sphere shown in the figure will be eliminated from the rest of the point cloud. In this manner, radius neighborhood removal eliminates the points out of the local intended surface.

Statistical method. Digitized point cloud are typically susceptible to varying point densities and also leads to sparse outliers which complicated the downstream processes (normal estimation, triangulation, curves and surface fitting, curvature estimation and so on) or even leads to failure. Statistical outliers removal is implemented to reduce the irregularities of a point cloud by computing the distribution of point to neighbors distances in the input dataset. For each point, the mean distance from it to all its neighbors are computed. By assuming that the resulted distribution is Gaussian with a mean and a standard deviation, all points whose mean distances are outside an interval defined by the global distances mean and standard deviation can be considered as outliers and trimmed from the dataset. Figure 2(c) shows the standard normal Gaussian distribution with corresponding coefficients and statistical percentage. The algorithm requires to define the coefficient value which is corresponding to the number of points to be deleted or not. The (1), (2) and (3) times standard deviation (σ) means about 68, 95, 99.7% of the points will be kept in the point cloud, respectively. Figure 3 shows an arbitrary plane object point cloud with outliers, and the treatment with different standard deviation coefficient values and the corresponding treated results. This method is robust and efficient outliers removal method and also used to reduce the number of points.

Fig. 3.

The working principle of statistical outliers removal with different number of standard deviation tolerance coefficients. The object is a plate. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

3.1.2. Cross-sectional point data extraction

Once the outliers are eliminated from the raw point cloud. The point cloud is sectioned by transversal and waterline planes to extract the corresponding section curves. For instance transversal section curves can be interpolated or approximated once the stations point cloud is properly extracted. The same holds for waterline curves. In this work, a simple procedure is proposed to extract and treat the section point cloud as shown in Figs 4 and 5. These include define the number of section planes, determine the point cloud around the section plane within the defined tolerance, and project the points to the center plane. For instance the user defines the axis (x – for transversal sections and z – for waterlines sections) and the desired number of sections. Then, the algorithm automatically extracts the sections points based on the defined diameter (tolerance zone) for example, for traversal sections $X (i + 1)$ – $X (i)$ . The extracted cross-sectional points are projected to the mean or center points to change the coordinate system from 3D to 2D as shown in Fig. 4. Therefore, it is easier to deal with 2D point cloud for further treatment and curves fitting. At this stage the waterlines and transversal sections point cloud are identified, but still needs more treatment. It is obvious that a wider tolerance zone implies lower accuracy of the result.

Fig. 4.

Cross-sectional points extraction method. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Fig. 5.

Cross-sectional points extraction algorithm chart.

3.1.3. Ordering the point cloud

Some of the point cloud pre-processing algorithms and the curve fitting process need strictly ordered point cloud. Therefore, four 2D point data ordering options are incorporated: ascending/descending, two variables ordering, center-points-angle method and nearest point method. Ascending/descending is the simplest method which orders based on the increment/decrement of one of the variable of the points (i.e. x or y), while two variables ordering considers the second variable too (i.e. based on x and then y). Center-points-angle method orders point cloud into clockwise or anti-clockwise based on the point cloud center of gravity. It orders based on the magnitude of the angles each points makes with the center point. This method is efficient for objects without occlusion. The center point can be manipulated by the user based on the complexity of the shape. Nearest point method is a robust and better compared to the above three methods. For open curves, the outer point should be first determined, and then an algorithm determines the nearest point to a current point. Once a nearest point is determined, then a point is deleted from the array of the point cloud. Based on this process, the points are ordered for pre-processing purpose or for curve fitting process as shown in Fig. 6.

Fig. 6.

Pre-processing (filtering, down-sampling and smoothing) of 2D cross-sectional point cloud algorithm chart. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

3.1.4. Cross-sectional filtering and smoothing of point data

At this stage, the 2D cross-sectional point cloud in all cross-sectional plane are extracted. The next step is to filter, down-sample and smooth the 2D point data for automatic curves interpolation or approximation. For these reasons three different filtering, smoothing and down-sampling options are incorporated in the developed methodology as shown in Fig. 6.

Mean method. The mean method works based on stepped increment and statistical mean of the data array in specified step/gap. For instance, for transversal section point cloud, the stepped incremental (S) is defined by the user and the points fall in that gap will be summed up and the mean of those points will be computed. $S (i) = Z (i + 1) - Z (i)$ , where $i = 0, 1, 2, \dots, n$ and where n is the number of steps. The mean point of the points between $Z (i + 1)$ and $Z (i)$ is computed but the initial and final points are always preserved. $Y (j) = Mean [x (j) + x (j + 1) + x (j + 2) + \dots + x (m)]$ , where $j = 0, 1, 2, \dots, m$ and m is the number of points fall in single step increment. The mean method is able to filter point cloud noise in 2D and also smooths. Proper definition of step incremental value resulted in good result, and too low value definition leaves noise and outliers and too high values can omit the details of the object. Figure 8(a) shows the results of a mean method with different step increment values. It is shown that $S = 4 mm$ is to high to catch the curvature of the curve and on the other hand $S = 1 mm$ is too low to eliminate unnecessary outliers. It is shown that $S = 2 mm$ sufficiently filters and smooths the point cloud for this specific test case.

Angle method. It is very fast and robust but requires pre-ordered point cloud as an input. The algorithm iterates through all points and checks the angle (β) between the three consecutive points $D (i - 1)$ , $D (i)$ and $D (i + 1)$ as shown in Fig. 7. If the angle is less than the default (90°) or user defined angle, then the algorithm eliminates $D (i)$ .

Fig. 7.

Filtering and smoothing using angle method: the principle. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Fig. 8.

The left figure (a) shows the result of mean method with different step increment values and the right (b) shows the result of angle method with different angles. In this figure the star points are a raw points and the dot points are the filtered point cloud with corresponding variable and methods. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

The same point cloud, used in mean method, is filtered using angle method as shown in Fig. 8(b), angle method is more stable and useful to eliminate impulse noise compared to mean method. In addition to filtering outliers, angle method smooth the point cloud. But proper angle should be defined to preserve the curvature or knuckle of the curves. Increasing the magnitude of an angle filters, smooths and reduces the number of points, but could be resulted in loss of geometric details. The possible maximum and minimum magnitude of the angle are 0° and 180°, respectively. Defining angle value as 180° deletes any point out of plane, while 0° does not affect the original point cloud.

Rectangle centroid method. Rectangular centroid method (2D voxel grid) is a 2D point cloud filtering and down-sampling method adapted from 3D voxel grid sampling algorithm in PCL. It creates a 2D rectangles over the point data based on user define length (L) and height (H) of the rectangle. Then, all the points fall in each rectangle are approximated by the centroid of the rectangle. It is efficient in down-sampling and regularization of point cloud, in addition to outliers filtering and smoothing. With increasing the rectangle dimension, the number of points gets reduced and regularized as shown in Fig. 9.

Fig. 9.

Rectangular centroid method with different rectangle size (3 mm × 3 mm with number of points reduced from 130 to 53 and with 3 mm × 6 mm reduced to 25 and with 3 mm × 10 mm reduced to 24). The input point cloud has 130 data points with artificially introduced noise and outliers. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

3.2. Curves fitting

The development of polynomial parametric representation has played a major role in advancing the field of computational geometry. Specially the introduction of well-known flexible polynomial parametric representations such as Bézier and B-Splines curves and surfaces increase the efficiency, capability and the geometric interpretations of polynomial parametric forms. Bézier and B-Spline curves have many nice properties for the curves design, but not able to represent the simplest curves: the circle, ellipses and other curves that are not represented by polynomials. Therefore both Bézier and B-Spline curves are generalized to rational Bézier curves and Non-Uniform Rational B-Splines (NURBS) respectively to enable the representation capable to manage simple curves mentioned above.

The mathematical description, advantages and limitations of B-Splines, NURBS curves and surfaces are not given in this work, interested might refer to [34,40,45]. This section introduces the techniques used to fit the points into transversal and waterline section B-Spline curves. Interpolation and approximation are the two well-known curves fitting techniques which used to fit curves to arbitrary set of geometric data, such as points and derivatives vectors. The input to a B-Spline interpolation/approximation algorithm usually consists of a set of data points. Thus, the first step is to find a set of parameters that can fixed these points at certain values. More precisely, if the data points are $D_{0}, D_{1}, \dots, D_{n}$ , then $n + 1$ parameters $t_{0}, t_{1}, \dots, t_{n}$ in the domain of the curve must be found so that data point $D_{k}$ corresponds to parameter $t_{k}$ for k between 0 and n. This means that if $C (u)$ is a curve that passes through all data points in the given order, then we have $D_{k} = C (t_{k})$ for all $0 ⩽ k ⩽ n$ .

There are infinite number of possibilities for selecting the set of parameter $t_{0}, t_{1}, \dots, t_{n}$ . However, poorly chosen parameters could be resulted in unpredictable result by affecting the shape of the curve [34,40,45]. Consequently, this affects the parametrization of the curves. As a result there are many parameter selection methods proposed in literature, which includes the uniformly spaced method, chord length method, centripetal method and universal method. For more details the reader could refer to [40,45].

3.2.1. Curve global interpolation

Taking the point sets $D_{0}, D_{1}, \dots, D_{n}$ and fit them with a B-Spline curve of degree p, where $p ⩽ n$ is an input. The parameter values and the knot vectors are determined using the parametric selection methods and knot vector generation, respectively. Once the knot vector and the degree p are determined, the only missing part is a set of $n + 1$ control points. Global interpolation is a simple way of finding these control points of the curves pass through all points as shown in Fig. 10. For detail mathematical description refer to [34,40].

Fig. 10.

Demonstration of curve interpolation. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

3.2.2. Curve global approximation

In interpolation, the curve passes through all given data points in the given order. An interpolating curve may wiggle through all data points rather than following the data polygon closely. The approximation technique is introduced to overcome this problem by relaxing the strict requirement that the curve must contain all data points. In global approximation, except for the first and last data points, the curve does not have to contain every point. To measure how well a curve can approximate the given data polygon, the concept of error distance ( $e_{r}$ ) is introduced. The error distance is the distance between a data point and its corresponding point on the curve as shown in Fig. 11. Thus, if the sum of these error distances is minimized, the curve should follow the shape of the data polygon closely. An interpolating curve is certainly such a solution because the error distance of each data point is zero.

Fig. 11.

Demonstration of curve approximation. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Given a set of $n + 1$ data points, $D_{0}, D_{1}, \dots, D_{n}$ , a degree p and a number h, where $n > h ⩾ p ⩾ 1$ , find a B-Spline curve of degree p defined by $h + 1$ control points that satisfies the following conditions: this curve contains the first and last data points (i.e., $D_{0}$ and $D_{n}$ ) and this curve approximates the data polygon in the sense of least square. Thus, approximation is more flexible than interpolation, because we not only select a degree but also the number of control points. For detail mathematical descriptions the reader might refer to [34,40].

3.2.3. Semi-automatic ship hull form curves interpolation and approximation

In the developed system, both interpolation and approximation curves fitting approaches are implemented to fit B-Spline curves to pre-processed point cloud. Once the point cloud is treated using the methods discussed in pre-processing section, the pre-processed point sets are fitted to the B-Spline curves using the interpolation or approximation algorithms implemented from Open CASCADE Technology library. Open CASCADE offers the possibility of interpolation with GeomAPI_Interpolate class and approximation with GeomAPI_PointsToBSpline from pre-processed and consistently ordered point cloud. Constrained B-Spline curve passing through the points of the input data, where the parameters of each of its points are given by the parallel table parameters. The resulting B-Spline curve will be $C^{2}$ continuous, except where a tangency constraint is defined on a point through which the curve passes. In this case, it could be decreased to $C^{1}$ continuity. Based on the defined parameters the class Geom_BSplineCurve returns a B-Spline curve. In this paper, a semi-automatic hull form cross-sectional curves fitting to point cloud is implemented as described in Algorithm 1 for interpolation. The approximation of cross-sectional curves follow the same procedure except the need for additional user inputs such as degree range (minimum and maximum), the error distance ( $e_{r}$ ) and continuity. The developed pre-processing methodology prepares a consistently filtered, smoothed and ordered inputs for interpolation and approximation. Once the above parameters are defined the points to curves approximation is performed automatically. In Algorithm 1, TopoDS_Wire and TopoDS_Compound are the classes from Open CASCADE Technology used to return wire and a compound of wires, respectively.

Algorithm 1.

The general algorithm layout of the developed system for transversal section curves interpolation

Once the desired methods and corresponding parameters for point cloud pre-processing are set. The cross-sectional curves (transversal and waterline sections) interpolation or approximation can be automatically computed with curves density and pre-processing parameters defined.

3.3. Surface generation

Even-though curves network based hull form surface fitting is the traditional method in ship CAD systems, the curves network method point cloud to NURBS surface fitting is not well studied. In this work, hull form reverse engineering is aligned with the traditional curves based surface construction. Once the point cloud is pre-processed using the described cross-sectional method, the B-Spline curves are interpolated or approximated based on the user preferences. With point cloud to ship hull form regular cross-sectional curves fitted, the surface fitting based on curves network is well studied and incorporated in marine CAD systems. In this work, Rhinoceros [42] is selected as it provides extensive NURBS surface fitting, many plug-in for different specific applications, and possibility to include own code through scripting language. It incorporates several NURBS fitting approaches based on curves network such as lofting, extruding, sweeping, revolving, patching and surface from curves network. From these possibilities, lofting, patching and surface from curves network are found to be feasible for hull form reconstruction from cross-sectional curves network.

3.3.1. Lofting

Lofting creates a smooth surface that blends between selected curves network. The resulting surface quality is strongly dependent on the difference between the number of control points of consecutive curves and the fairness of the curves. The consecutive curves control points number closeness promise a better surface quality in lofting and the curves should be selected in the consistent order. The limitation of lofting is that, it does not manage the crossing curves.

Fig. 12.

NURBS surface generation using patching method (left) and surface from curves network method (right). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

3.3.2. Patching

Patching creates a trimmed NURBS surface from curves network. If the boundary curves (exterior curves) are closed, then the patching trims the surface using the boundary curves automatically. For instance in Fig. 12(left) four closed boundary curves are created, and the rest curves (interior curves) help to catch the curvature of the surfaces. In this case, the user does not require to define the ordering of the curves network. The patching method builds the surface patch by first finding the best fit plane through the selected and sampled points along curves. Then the surface deforms to match the points and sampled points. It also offers the possibility to constrain the surface by defining the neighboring surface edge which fits the tangent direction of the surface. The bold curve in Fig. 12(left) shows the selection of the surface edge to keep the tangency between consecutive surfaces.

3.3.3. Surface from curves network

Surface from curves network method creates a NURBS surface from network of crossing curves. This method offers automatic creation of patch boundary (edge curves) which makes it easy and fast compared to the patching method. The edge curves are selected by user and used to set the allowable tolerance the surface may deviate from the edge curves. The label A, B, C, D in Fig. 12(right) shows the edge curves of a surface to be fitted. Interior curves set the allowable tolerance the surface may deviate from the interior curves. Similar to patching method, surface from curves network offers the use of curves geometry or existing surface edges as a boundary wire (edges). This functionality helps to ensure the continuity and smoothness between consecutive surfaces, therefore it is highly recommended to use surface edges rather than curve geometry. The label D (bold) in Fig. 12(right) shows the selection of the surface edge to create continuity between successive surface patches.

4. Case study

This section illustrates the developed RE methodology against ship hull form point cloud data. The case study is divided into two based on their input sources: artificially produced point cloud from existing geometric surface and measured data from ship model.

4.1. Fitting on produced point data

To check the efficiency and robustness of the developed methodology, it should be tested against different types of hull forms. Hence, a software tool which reads existing hull form CAD data (IGES file format) and generates point cloud with random noise and outliers is developed. The developed tool (converter) helps to produce point cloud from different test cases (ship hull forms). This part of the case study is demonstrated with a ship hull form represented with around half a million point cloud including artificially introduced noise and outliers.

The developed RE methodology reads point cloud from (*.txt or *.ply or *.pcd) and offers the user to select outliers removal methods (bounding domain, conditional, radius neighborhood or statistical). It is possible to use all methods or select the desired one from the list. At this stage the outliers should be eliminated as shown in Fig. 13.

Fig. 13.

Hull form (bow region) before and after pre-processing of 3D point cloud which includes outliers removal, filtering and down-sampling.

Once the outliers are removed the developed system automatically divides the hull form into five regions based on two user defined critical points (bow (bcp) and stern (scp)) as shown in Fig. 14. The definition of the two critical points avoid the difficulty of automatic transversal section curves fitting, and enable the possibility to fit more denser curves to high curvature regions (such as bow and stern). On the receipt of five regions, the transversal sections points are extracted. Hull form division is not necessary for the extraction of points in waterline sections. The extracted points should be treated based on the described procedure in point data pre-processing section.

Fig. 14.

Ship hull form point cloud division. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

The developed pre-processing generates transversal and waterline sections as shown in Figs 15 and 16, respectively. In addition to transversal and waterline sections, centerline and deck points are extracted using the boundary extraction method implemented in PCL specifically Concave method [41].

Fig. 15.

Extracted transversal sections point cloud.

Fig. 16.

Extracted waterline sections point cloud.

The consistent pre-processing of point cloud eases the curves interpolation and approximation. The interpolation and approximation functions are implemented in the developed methodology, and both are applicable for the curves fitting as the point cloud pre-processing could filter and smooth the point cloud successfully. In some cases, if the section points are denser and not well smoothed, the approximation could be preferred while for well-treated point cloud, the interpolation function works well. In this work, the deck and centerline points are extracted to increase the accuracy of the outer boundary. Here one can introduce prior knowledge to improve the accuracy of reconstruction. For centerline and deck curves fitting the interpolation is generally preferred.

After all curves are interpolated or approximated they all put together as shown in Fig. 17 and ready for surface fitting.

Fig. 17.

The transversal, waterline sections with centerline and deck curves fitted using the developed method. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

In this method the qualities of the interpolated and approximated curves are highly dependent on the point cloud pre-processing. However, interpolation or approximation functions could be used interchangeably for transversal and waterline section curves as the pre-processing treat the point cloud towards the curves network fitting. The surface fitting using lofting, patching and surface from curves network methods are experimented based on the fitted cross-sectional curves. The traditional lofting only considers either transversal or waterline sections at a time. This is the disadvantage of lofting for the intended curves network based reverse engineering. However, it is possible to use transversal or/and waterline section curves accordingly. Figure 18 shows how transversal and waterlines section curves could be used to generate NURBS hull form surfaces using traditional lofting. The illustrated method is recommendable to generate hull form surface from the curves network.

Fig. 18.

Hull form NURBS surfaces generated from transversal and waterline section curves using lofting. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

The surface generation from curves network using patching method is time consuming because the user has to create the boundary curves manually as shown in Fig. 19, but the surface from curves network method offers automatic creation of boundary curves which accelerates the time required to generate surfaces from curves network. It also provides better surface continuity compared to lofting and patching as shown in Figs 20 and 21.

Fig. 19.

Surface creation process using patching method from curves network (transversal, waterline sections, centerline and deck curves). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Fig. 20.

Surface generation process using surface from curves network method. The label A, B, C, D show an automatic creation of boundary curves of the patch to be created. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

Fig. 21.

Ship hull form NURBS surface reconstructed from curves network using surface from curves network method.

Fig. 22.

Model ship reverse engineering using developed methodology. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/ISP-150115.)

4.2. Fitting on measured point data

A small scale model ship (length overall = 40 cm) is scanned using DAVID Laserscanner [9] at our department. The measurement is performed from four directions (front, back, right and left side). The four patch of point cloud are transformed to common global coordinate system. The registered point cloud is used as an input to the developed methodology. This measured data is tested against the developed method, using similar procedure described above and the successive results are shown in Fig. 22. The developed method shows similar behavior against artificially generated and measured data, but there are some ripple in the generated surfaces. The ripple in the surface is attributed to inaccuracies in laser scanner to objects reference during measurement and poor registration between measured point cloud patches. This implies that, the measurement techniques and the registration affect the quality of the downstream processes such as point cloud pre-processing, curves and surface fitting results.

5. Merits and limitations

Curves network based reverse engineering offers considerable advantages. The method finds a good reason to be preferred for hull form reverse engineering, because, curves (hull lines plan) based NURBS surface generations are state of the art in maritime industries. Hull form surface NURBS representation is very popular in maritime industries and offers many advantages [28,43,52]. However, there are limitations, especially with regards to its unsuitability for direct integration into downstream applications (such as computational fluid dynamics, computational solid dynamics, etc.) because of its topological limitations [1,7,44]. As part of our research, an automatic ship hull form CAD repairing, region identification and domain preparation techniques are developed, the reader might refer to [6,10] for contribution.

Depending on the measurement quality and density, it is usually challenging to properly extract the boundary edge of the point cloud. In this work, ship hull form centerline and deck line curves are extracted precisely, however preservation of the knuckles while dealing with an automatic spline fitting is challenging. Even though the point cloud pre-processing algorithms are implemented in such a way that they preserve features. The curves and surface fitting usually lead to loss of sharp edges.

With regards to hull cross-sectional curves extraction, the method extracts transversal and waterline section curves automatically, however the buttocks sections extraction is challenging. This attributed to the slight change in inclination specifically in the aft and fore regions of the hull form.

6. Conclusion

Reverse engineering finds several applications in maritime industry as in any industries such as redesign, maintenance, retrofit and historical archive. Moreover, the successive tightening of environmental standards makes the reverse engineering practices essential to retrofit the existing vessels. Therefore the development of precise, efficient and cost saving maritime structures reverse engineering is inevitable. The developed methodology presents a B-Spline curves network (transversal and waterline sections) of ship hull form from unorganized point cloud. With a receipt of consistently aligned point cloud from various patches of 3D point cloud data views, the develop methodology provides efficient and time saving reconstruction strategy. The method quickly reduces a large range of data to manageable size, which is essential for large objects like ship hull form. In CAD systems, the NURBS surface design based on curves network is well developed, which makes the developed method preferable and easier. The transversal sections, waterline sections, centerline and deck curves are successfully generated using either interpolation or approximation. The efficient point cloud data pre-processing enable either interpolation or approximation to be used interchangeably. But, with extreme difference in density and large irregularities in an input data, the user is recommended to select approximation. The performed case studies show that the developed methodology has significant contribution to the hull form reconstruction processes. Because ship hull form NURBS generation from curves network is well developed. The generated curves networks are tested against three existing surface generation method (lofting, patching and surface from curves network). The study reveal that the surface from curves network method provides better surface quality and also safe time.

Generally with the inclusion of prior knowledge and further development in the developed reconstruction process, the method will be a promising strategy to re-engineer the ship hull form.

7. Future works

Despite its suitability and ability to reconstruct hull surface, the proposed approach has limitations in preserving detail features such as knuckles, holes, etc. Recent reverse engineering studies suggest to incorporate application specific knowledge based and certain feature sensitive reconstruction approaches [4,17]. Therefore, the proposed framework could be improved if equipped with additional feature sensitive geometric approaches and integrated with knowledge assisted reverse engineering techniques. These developments will be considered for further accuracy and robustness in the future research at our institute.

References

[1]

Abt,

Bergmann and

Harries, Domain preparation for RANSE simulations about hull and appendage assemblies, Ship Technology Research 59(3) (2012), 24–37.

[2]

Amenta,

Bern and

Kamvysselis, A new Voronoi-based surface reconstruction algorithm, in: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’98, Vol. 26, 1998, pp. 415–421.

[3]

Benko,

Kosa,

Varadya,

Andorb and

Martin, Constrained fitting in reverse engineering, Computer Aided Geometric Design 19(3) (2002), 173–205.

[4]

Berger,

Tagliasacchi,

L.M.

Seversky,

Alliez,

J.A.

Levine,

Sharf and

C.T.

Silva, State of the art in surface reconstruction from point clouds, in: Eurographics 2014 – State of the Art Reports,

Lefebvre and

Spagnuolo, eds, The Eurographics Association, 2014.

[5]

Bole, Regenerating hull design definition from poor surface definitions and other geometric representations, in: COMPIT 2014, Redworth, UK, May 2014, 2014.

[6]

Bronsart,

D.M.

Edessa and

Kleinsorge, A contribution to automatic ship hull form cad data repairing, in: Proceedings of the PRADS2013, South Korea, 20–25 October 2013, 2013.

[7]

Bronsart,

Knieling and

Zimmermann, Automatic generation of a panel-based representation of ship hulls for wave resistance calculations, in: Proceedings, PRADS 2004, Schiffbautechnische Gesellschaft, Hamburg, 2004.

[8]

Budak,

Vukelić,

Bračun,

Hodolič and

Soković, Pre-processing of point-data from contact and optical 3D digitization sensors, Sensors 12(1) (2012), 1100–1126.

[9]DAVID 3D Solutions GbR, David Laserscanner homepage, Internet, 2014.

10.

[10]

D.M.

Edessa,

Kleinsorge and

Bronsart, Assuring quality ship hull form representation for downstream applications, in: Maritime Technology and Engineering,

Guedes Soares and

T.A.

Santos, eds, Taylor & Francis Group, London, 2014.

11.

[11]

Gerbino,

Renno and

Papa, Two reverse engineering methods for the reconstruction of an high speed craft surface: A comparison, in: International Design Conference-Design, 18–21 May 2004, 2004.

12.

[12]

B.F.

Gregorski,

Hamann and

K.I.

Joy, Reconstruction of B-spline surfaces from scattered data points, in: Proceedings of Computer Graphics International, 2000, pp. 163–170.

13.

[13]

Guennebaud and

Gross, Algebraic point set surfaces, ACM Transactions on Graphics 26(3) (2007), 1–9.

14.

[14]

J.G.

Hayes and

Halliday, The least-squares fitting of cubic spline surfaces to general data sets, IMA Journal of Applied Mathematics 14(1) (1974), 89–103.

15.

[15]

Hollenbach and

Reinholz, Hydrodynamic trends in performance optimization, in: 11th International Symposium on Practical Design of Ships and Floating Structures, Brazil, 2011.

16.

[16]

Hoppe,

DeRose,

Duchamp,

McDonald and

Stuetzle, Surface reconstruction from unorganized points, in: Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’92, Vol. 26, 1992, pp. 71–78.

17.

[17]

Hung Truong, Knowledge-based 3D point clouds processing, PhD thesis, Universite de Bourgogne, 2014.

18.

[18]

Karniel,

Belsky and

Reich, Decomposing the problem of constrained surface fitting in reverse engineering, Computer Aided Geometric Design 37(4) (2005), 399–417.

19.

[19]

Kazhdan,

Bolitho and

Hoppe, Poisson surface reconstruction, in: Eurographics Symposium on Geometry Processing, 2006, pp. 61–70.

20.

[20]

H.J.

Koelman, Application of a photogrammetry-based system to measure and re-engineer ship hulls and ship parts: An industrial practices-based report, Computer-Aided Design 42(8) (2010), 731–743.

21.

[21]

Labatut,

J.-P.

Pons and

Keriven, Robust and efficient surface reconstruction from range data, Computer Graphics Forum 28(8) (2009), 2275–2290.

22.

[22]

J.-Y.

Lai and

W.-D.

Ueng, Reconstruction of surfaces of revolution from measured points, Computers in Industry 41(2) (2000), 147–161.

23.

[23]

Leal,

Leal and

J.W.

Branch, Simple method for constructing NURBS surfaces from unorganized points, in: Proceedings of the 19th International Meshing Roundtable, 2010.

24.

[24]

N.E.

Leal Narváez,

E.A.

Leal Narváez and

J.W.

Branch, Automatic construction of NURBS surfaces from unorganized points, Dyna 78(166) (2011), 133–141.

25.

[25]

Levoy,

Pulli,

Curless,

Rusinkiewicz,

Koller,

Pereira et al., The digital Michelangelo project: 3D scanning of large statues, in: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’00, 2000, pp. 131–144.

26.

[26]

Liao,

Xiao,

Jin and

Fu, Efficient feature-preserving local projection operator for geometry reconstruction, Computer-Aided Design 45(5) (2011), 861–874.

27.

[27]

Lipman,

Cohen-Or,

Levin and

Tal-Ezer, Parameterization-free projection for geometry reconstruction, in: ACM SIGGRAPH 2007 Papers, SIGGRAPH’07, Vol. 26, 2007, pp. 173–205.

28.

[28]

Lu,

Zhang and Yanlin , Representation for characteristic curves of hull form using immune genetic algorithm based on NURBS with path curve parameterization method, in: Proceedings of the Twenty-Fourth International Ocean and Polar Engineering Conference, Busan, Korea, 15–20 June 2014, 2014.

29.

[29]

Menna, Underwater photogrammetry for 3D modeling of floating objects: The case study of a 19-foot motor boat, in: Sustainable Maritime Transportation and Exploitation of Sea Resources, 2012.

30.

[30]

Menna,

Nocerino and

Scamardella, Reverse engineering and 3D modelling for digital documentation of maritime heritage, in: International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-5/W16, ISPRS, Trento, Italy, 2011.

31.

[31]

Menna and

Troisi, Photogrammetric 3D modelling of a boat’s hull, in: Proceedings of the Optical 3-D Measurement Techniques VIII, ETH Zurich, 2007.

32.

[32]

Menna and

Troisi, Low cost reverse engineering techniques for 3D modelling of propellers, in: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission V Symposium, Vol. XXXVIII, Part 5, Newcastle upon Tyne, UK, 2010.

33.

[33]

Troussier,

Bricogne,

Durupt,

Belkadi and

Ducellier, A knowledge-based reverse engineering process for CAD models management, in: Proceedings of IDMME – Virtual Concept, 20–22 October 2010, 2010.

34.

[34]

Nowacki,

M.I.G.

Bloor and

Oleksiewicz, Computational Geometry for Ships, 1st edn, World Scientific Publishing Co., Inc., Singapore, 1995.

35.

[35]

Ohtake,

Belyaev,

Alexa,

Turk and

H.-P.

Seidel, Multi-level partition of unity implicits, in: ACM SIGGRAPH 2003 Papers, SIGGRAPH’03, Vol. 22, 2003, pp. 463–470.

36.

[36]Open CASCADE S.A.S., Open CASCADE homepage, Internet, 2015.

37.

[37]

Park, An approximate lofting approach for B-spline surface fitting to functional surfaces, International Journal of Advanced Manufacturing Technology 18(7) (2001), 474–482.

38.

[38]

I.K.

Park,

I.D.

Dong Yun and

S.U.

Lee, Constructing NURBS surface model from scattered and unorganized range data, in: Proceedings, Second International Conference on 3-D Digital Imaging and Modeling, 1999.

39.

[39]

F.L.

Pérez,

J.A.

Clemente,

J.A.

Suárez and

J.M.

González, Parametric generation, modeling, and fairing of simple hull lines with the use of nonuniform rational B-spline surfaces, Journal of Ship Research 52(1) (2008), 1–15.

40.

[40]

Piegl and

Tiller, The NURBS Book, 2nd edn, Springer, New York, 1997.

41.

[41]Point Cloud Library, Point Cloud Library homepage, Internet, 2015.

42.

[42]Robert McNeel & Associates, Rhinoceros homepage, Software, 2015.

43.

[43]

S.M.

Shamsuddin,

M.A.

Ahmed and

Samian, NURBS skinning surface for ship hull design based on new parameterization method, International Journal of Advanced Manufacturing Technology 28 (2006), 936–941.

44.

[44]

Sharma,

T.-W.

Kim,

Storch,

H.(J.J.)

Hopman and

S.O.

Erikstad, Challenges in computer applications for ship and floating structure design and analysis, Computer-Aided Design 44 (2012), 166–185.

45.

[45]

C.-K.

Shene, Introduction to computing with geometry notes, Internet, 2015.

46.

[46]

Shi,

Wang and

Yu, A practical construction of G1 smooth biquintic B-spline surfaces over arbitrary topology, Computer-Aided Design 36(5) (2004), 413–424.

47.

[47]

Sotoodeh, Outlier detection in laser point clouds, in: IAPRS, Vol. XXXVI, Part 5, Dresden, 25–27 September 2006, 2006.

48.

[48]

W.-D.

Ueng,

J.-Y.

Lai and

J.-L.

Doong, Sweep-surface reconstruction from three-dimensional measured data, Computer-Aided Design 30(10) (1998), 791–806.

49.

[49]

Vanco,

Hamann and

Brunnett, Surface reconstruction from unorganized point data with quadrics, Computer Graphics Forum 27(6) (2008), 1593–1606.

50.

[50]

Wang,

Yub,

Zhangc,

Weid,

Tana,

Dai and

Zhange, Robust reconstruction of 2D curves from scattered noisy point data, Computer-Aided Design 50 (2014), 27–40.

51.

[51]

Weiss,

Andor,

Renner and

Varady, Advanced surface fitting techniques, Computer Aided Geometric Design 19(1) (2002), 19–42.

52.

[52]

A.S.

Wen,

S.M.H.

Shamsuddin and

Samian, An optimized ship hull fitting approach using NURBS, in: Proceedings of the Postgraduate Annual Research Seminar, 2006.

53.

[53]

Xiao,

Zheng,

Miao,

Zhao and

Peng, A unified method for appearance and geometry completion of point set surfaces, The Visual Computer 23(6) (2007), 433–443.

54.

[54]

D.-J.

Yoo, Three-dimensional surface reconstruction of human bone using a B-spline based interpolation approach, Computer Aided Geometric Design 43(8) (2011), 934–947.