Boletín Técnico, Vol.55, Issue 1, 2017, pp.183-192
Non-Realistic Shape Modeling Method to the Product Design Based
on Graphic Intelligence
Dan Sun
College of Art, Northeast Agricultural University, Heilongjiang, Harbin, 150039, China
Abstract
This paper presents a method to design a non-realistic form line and a ball modeling method for product design
based on the graphic intelligence to realize a simple and fast three-dimensional model prototype structure. With
a non-realistic form line, this paper firstly uses the circle or ellipse to the approach. Then, it sets the third
dimension of the parameters for each circle or ellipse to obtain the corresponding super-ellipsoidal sphere.
Finally, the field of all morphological balls is mixed and the shape parameters of all non-realistic morphological
balls are optimized to obtain a graphic intelligent surface of the analytic non-realistic shape ball, which can be
easily modified by adjusting the shape of the ball or the shape on the surface to modify the form of different
parts on the model. It is different in the projection plane to outline the non-real form. The method is designed to
be widely used in prototyping of the conceptual design phase in the field of computer graphics or computer
aided design.
Key words: Non-realistic Form Line, Graphic Intelligent Surface, Non-Realistic Shape Sphere, Shape
Approximation.
1. INTRODUCTION
Surface modeling technology is the basis of computer aided design (CAD), computer aided manufacturing
(CAM) and graphics, and its research begins with the polynomial approximation and interpolation techniques.
Finally, Bézier and B-spline curves and surface modeling techniques are the parametric surface modeling
technology. Although the parametric surface modeling technology has achieved great success, but due to the
inherent defects in the parameters, the technology is still inadequate. To this end, from 1980s, there was another
surface modeling F (x, y, z)-Iso=0. By adjusting the value of Iso, we can get the value of Iso, and we can get the
surface of the object by implicit function equation. Each surface is called the equipotential surface, and the
equation F (x, y, z) is called the field function. By defining different field functions and mixing them, various
complex surfaces can be generated.
The use of graphical intelligent surface modeling can ensure the continuity and smoothness of the model,
which can easily achieve the deformation of the shape in the results. Blinn firstly proposed a special graphical
intelligent surface modeling technology in the field of computer graphics, which was called the Blobby model
(Blinn, 1982). Subsequently, Nishimura et al. proposed the Metaball model (Nishimura, Hirai, Kawai, Kawata,
Shirakawa and Omura, 1985), and Wyvill proposed the Soft Object model (Wyvill, McPheeters and Wyvill,
1986). These models are called non-realistic morphological sphere models whose implicit functions are the sum
of some radial symmetric functions, and these radial symmetric functions have the geometrical shape of the
Gaussian function. Used in various fields of computer graphics, Tatsumi gave the use of the non-realistic shape
ball modeling techniques in cod liver modeling (Tatsumi, Takaoki, Omura and Fujito, 1990). Muraki used the
Blobby model for three-dimensional object modeling (including human face modeling) (Muraki, 1991). Max
and Wyvill used the Soft Object to draw the corals (Max and Wyvill, 1991). Payne and Toga adopted the
distance field to generate the rat brain model (Payne and Toga, 1992). Wyvill applied Soft Object to simulate
lightning (Reed and Wyvill, 1994). Tsingos et al. overcame the shortcomings of the method in Document
(Muraki, 1991), and proposed a quasi-automatic method of reconstruction of the non-realistic morphological
sphere model (Tsingos, Bittar and Gascuel, 1995).
In the same year, Bittar et al. Put forward a method of fully automatic non-realistic morphological ball
graphical surface reconstruction (Bittar, Tsingos and Gascuel, 1995). However, this method is unstable and
requires the user to specify the appropriate axis resolution, otherwise it will generate an error. The results of the
approximation of the central spherulites are used to reconstruct a graphical intelligent surface approximating a
given model and to simulate the fluid motion effects (Jin, Liu, Wang, Feng and Sun, 2005). In these applications,
the isomorphic kernel functions, such as the sphere function, are used to produce larger aliasing due to the
isotropic nature of the sphere, and in order to reduce this error, Liu et al. (Liu, Jin, Wang and Hui, 2007)
proposed the use of ellipsoid as the original body to construct the non-realistic shape of the ball graphics
intelligent surface. This algorithm not only reduces the number of non-realistic shape of the ball, but also
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improves the accuracy of approximation, getting a better approximation results. However, in this paper, we
extend the ellipsoidal non - realistic shape sphere model, and use the hyper - quadratic surface as the original
body to model the ellipsoid non - realistic shape sphere model.
In recent years, researchers have done a lot of work in developing intuitive rapid modeling interactive
platforms, making it easier to prototype design work. In these free-form modeling systems that rely on sketches,
various model shape representations are used, including the triangular mesh (Igarashi, Matsuoka and Tanaka,
1999) and subdivision surface (Igarashi and Hughes, 2003). Teddy (Igarashi, Matsuoka and Tanaka, 1999) is the
first free-form modeling system that relies on the sketch concept, which generates a closed triangular mesh
model by the user's non-realistic shape line. But, the Teddy system does not support any combination of
independent components, which can’t generate extrusion components, and can’t build a genus greater than 0. On
the basis of Teddy, Igarashi (Igarashi and Hughes, 2003) relied on the local quadratic graphics intelligent
surface with approximation for re-grid, which can get smoother results.
In this paper, our goal is to apply the nonsense form vector graphics surface to the modeling work that
relies on any 2D non-real-looking form line, providing an intuitive and fast modeling technique that enables
quasi-swept adult modeling and local. We use the elliptical set to approximate the non-realistic form of the line.
To rely on this approximation, if we want to modify the shape of the model, we only need to change its close
concentration of the circle or the oval.
2. SUPER-QUADRATIC SURFACE NON-REALISTIC SHAPE BALL MODEL
Given a point set S  R3 , it is a ci  S , f i : R 3  R of kernel function for each point, which represents the
potential field generated by the point. If p is a point in the R3 of Euclidean space, the total field at point p in
point set S can be obtained by equation (1):
(1)
F  p    i f i  ci , p 
i
F  p   t  0 is defined an equipotential surface with a threshold of t.
Blinn (Blinn, 1982) used a global kernel function in his non-realistic morphological sphere model, which is
a function of zero at infinity, so the computation is very large. In order to increase the computational speed, f i
is usually defined as a local support (2). Using a quadratic polynomial function, Wyvill gave a quadratic
polynomial function in (Wyvill, McPheeters and Wyvill, 1986), using a quartic polynomial function as a
nucleus in our algorithm, as in the case of Nishimura (Nishimura, Hirai, Kawai, Kawata, Shirakawa and Omura,
1985) by a quadratic polynomial function:
2

ri 2 
1 
 , others ri   0 , Ri 
f i  p    Ri2 
(2)

others
0 ,
In the equation (2), ri  d  p,ci  returns the Euclidean distance from the given point p to the ci center of
the i-th non-realistic shape sphere, and we define the influence area of the non-realistic shape sphere. The
graphic intelligent surface is defined by a kernel function. In the general case, the original body of the nonrealistic shape ball graphics intelligent surface is a sphere, which is called a ball-type non-realistic form of the
ball model. Although the ball-type non-realistic shape of the ball model can be approximate the surface of many
objects, in order to improve this situation, Liu et al. (Liu, Jin, Wang and Hui, 2007) proposed the use of ellipsoid
as the original body to construct the non-realistic shape of the ball pattern. Because of the isotropic nature of the
sphere, it does not represent the sharp or flat features well. However, in order to be able to carry out the more
flexible modeling, this paper extends the ellipsoidal non-realistic morphological sphere model, and uses the
super-quadratic model of the ellipsoid non-realistic shape sphere model. Surface is viewed as a primitive body.
Due to the anisotropy of the super-quadratic surface, the field value of the midpoint of the space can not be
simply calculated by using the formula (2). For convenience, we modify the formula (2) as follows:
1   2  2 , others  0,1
i
i
fi  p   
others
0,
(3)
i is the space point p to the i-th of the relative distance of non photorealistic form on the center of the
sphere. For sphere, i2  ri 2 Ri2 is taken. For the standard spheroid, points in space in the presence of field
values can be calculated by formula (4) into the formula (3):
2
2
2
2
2
i2   x  xci  Ri,x
  y  yci  Ri2,y   z  zci  Ri,z
(4)
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However, in the practical applications, the original bodies are not all standard ellipsoids, and their three
axes are arbitrary orthogonal unit vectors. In order to calculate the spatial point in the potential field defined by
this type of ellipsoidal primitive, we establish a local coordinate system for each Vi,a ,Vi ,b ,Vi ,c of ellipsoid, the
center of the ellipsoid is the origin of the coordinate system, and the three axes of the ellipsoid are the three axes
of the coordinate system, so that we will set the field value of any ellipsoid (4) , which can be modified into the
following form:
i2   ri cos   
2
Ri2,a   ri cos    
2
2
Ri,b
  ri cos    
2
2
Ri,c
(5)
Among them,  Ri ,a , Ri ,b , Ri ,c  is defined as the ellipsoidal influence area of the non-realistic shape sphere,
which is the angle between the  ,  ,   vector and the Vi,a ,Vi ,b ,Vi ,c vector. We make Vi , p as the unit vector of
the ci p of vector.
cos    Vi , p  Vi,a ,cos     Vi ,p  Vi,b ,cos     Vi , p  Vi,c ,
2
2
 cos     cos       cos   
2
(6)
 1 shows the formula (5), the formula (6) into the formula (3), and
you can calculate the spatial point p at the field value.
By the above results analogy, we can get any point p in space to the super-quadratic surface of the original
center to the relative distance calculation formula:
i2   ri cos   
na

Rin,aa  ri cos   

nb

Rin,bb  ri cos   

nc
Rin,cc
(7)
 na ,nb ,nc  is the number of superquadric modeling, formula (6) and formula (7) are substituted into the
formula (4), the calculated value is the p of spatial point in the super-quadratic surface of the original body
which is defined by the field value in the field. For each superquant surface primitive, there are 11 free variables:
x
ci
, yci , zci , Ri ,a , Ri,b , Ri,c ,na ,nb ,nc , ,  ,
 ,  
is defined as the direction of the superquadratic surface by using these free variables to adjust the
shape of the non-realistic shape of the ball.
From the formula (7), when it is na  nb  nc  2 , it is easy to know that when it is na  nb  nc  2 , it
defines an ellipsoid primitive body. When it is Ri ,a  Ri ,b  Ri ,c  Ri , a ball initial body is defined.
3. THE GRAPHIC INTELLIGENT SURFACE OF THE NON-REALISTIC SHAPE BALL BY THE
NON-REALISTIC FORM
Given a non-realistic form line, a non-realistic morphological line can be constructed using a non-realistic
morphological ball styling system, which can be skipped by the user through a mouse or by extracting a nonrealistic shape line of a two-dimensional image. Through the interaction editor, we use a simple polygon to
represent the non-real form of the line. In order to generate a simple polygon from the shape of a non-realistic
shape on the graphical surface, we have the following steps to determine the form of non-realistic shape in the
ball graphics intelligent surface. The non-realistic form of the ball and its parameters is as follows: Firstly,
through the bound Delaunay triangulation, we can extract the non-real shape of the axis of the line. Then, we
place in the axis of the original two-dimensional body (circle or oval) and the size of the original. Finally, in
order to generate a three-dimensional model, each two-dimensional primitive corresponds to a threedimensional primitive body, through the numerical optimization to determine the most of each non-realistic
shape of the ball, which is the most excellent parameter value.
3.1. The Elliptical Approximation of the Non-Realistic Morphological Lines
In Section 2.1, we use the circle as the primitive to approximate the non-realistic form of the line. However,
the shape of the circle as the original body has some limitations, and each of the original round primitive is only
in a dimension to ensure that the original body is close to the non-realistic form of the body we want to shape. In
actual use, in order to make the final model smooth, we usually need to use the node density that has the
relatively high axis and the appropriate interpolation, which will lead to the final system of the non-realistic
shape of the ball more. In Figure 1(a), we only use the original body 1 and the original body 3, which can not
achieve the desired effect. We must add a new primitive body 2 and try to use the ellipse as the original body to
the non-realistic shape line approximation. Using the ellipse as the original body, each primitive can be made
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close to the object to be shaped in two dimensions (i.e., the long and short axes of the ellipse), so that the
number of primitives can be effectively reduced as shown in Figure 1 (b). It shows that the original body 1 and
the original body 3 change in another dimension. You can achieve the desired effect without adding the original
body 2, which can effectively reduce the latter part of the optimization and drawing of the workload.
(a) Circular approximation
(b) Ellipse approximation
Figure 1. Circular approximation and elliptic approximation of the non-realistic morphology lines
3.1.1. Ellipse Generation Based on the Axle Wire
The elliptic generation algorithm, which relies on the central axis, is improved on the basis of the round
generation algorithm. When we generate the initial circle, we transform the circle to obtain the ellipse. In order
to realize this deformation process, we must determine the direction of ellipse growth, that is, Elliptical long
axis direction and growth amount. It is assumed that the center of the ellipse to be processed is the c of node on
the central axis, where the initial radius of the circle is r, and the neighboring nodes are r, s and t (the central
axis algorithm determines each Axis nodes with no more than 3 adjacent nodes), with the b=r of short axis
length and the corresponding p1 , p2 , p3 . to the three vertices of the triangular plate. Firstly, the vector quantity
between the node c and the node v (v=r, s, t) is used as the direction vector of the elliptical long axis, and the
Va   r  v  r  v of unit vector is the vector direction perpendicular to the vector. Then, the length of the long
axis a  r   is increased until the ellipse encounters another sampling point except the p1 , p2 , p3 . ellipse is
the increment of the major axis of the ellipse. To determine an optimal  , we calculate each point x on the nonrealistic form line, and the length of the major axis is the axial length:
  x 

x  c    x  c   Va 
b2    x  c   Va 
2
2
b  r
(8)

The optimal  is the  opt  min   x   x  c   Va  0 . According to each effective node in the axle wire,
for adjacent node v (v=r, s, t), a candidate ellipse is produced and we finally select the largest area of the ellipse
as the center of the ellipse in the node.
In some cases, the primitive body is generated with a large degree of redundancy, and it is necessary to
filter the contribution of each ellipse to the adjacent ellipse. The specific strategy is to assume that ellipse A and
ellipse B are the adjacent ellipses. The long axis direction of A and B is the same, it is ra  rb  (  is a smaller
positive floating point number and ra ,rb is the minor axis of A and B). It is dis  ra  rb or dis  rb ra (dis is the
center distance of A and B, and ra and rb is the long axis of A and B) to cancel the ellipse with small
contribute to the oval.
In practical applications, we find that if the radius of the initial circle is taken a miniature parameter of 0.95,
that is, rnew  0.95rold . To make the ellipse more effective extension of the long axis, the contribution for each
elliptical primitive body is greater to the object, to get more ideal effect.
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3.1.2. Elliptical Generation Based on Sampling Points
We obtain the elliptical decomposition approximation of a two-dimensional contour, and select the original
data point p to increase (elliptical) until we reach another original data point q. We take the center c of the
ellipse, and the vertical direction of cp continues to increase (ellipses) until the third original data point s is
found. p, q and s determine an elliptical initial body. We repeat the previous steps for all the original data points
in turn, to get all the elliptical primitive, as shown in Figure 2.
(a) It swells in the opposite direction
to the p point until the point q
(b) touches the long axis of the ellipse in the
direction perpendicular to the normal
direction until it touches the point s .
Figure 2. Schematic diagram for ellipse generation ( p , q and s determine a candidate elliptical
primitive).
In order to ensure that the ellipse is in the process of generating ellipses to avoid whether the ellipse is out
of the two-dimensional shape of the line and the same line with the elliptical intersection operation, we have the
non-realistic shape line intensive sampling of the original data points as a generation elliptical seed point. It
starts from point p, estimates from a normal point n p , and defines a circle of radius r along the negative normal
direction. In order for p to be on the circle, the center position is c  p  rn p , so that the second point q is on the
non-realistic form line and it is on the circle. The point q may be the original data point or the sampling point.
For each point x, the r(x) of normal direction of circle is confirmed by the interpolating point p, x and n p of
the normal direction as follows:
r  x 

x p
2
T
2  x  p  np
(9)

We will continue to increase the r of circle as ropt  min r  x   x  p  n p  0 after finding the largest
inscribed circle with two points on the circle. We will use the center c of the inscribed circle as the center of the
ellipse on the short axis direction. n p is along the n p vertical direction of the growth of the ellipse until another
point s is found on the ellipse. At this point, we can rely on the central axis of the ellipse generation algorithm to
determine the growth of the ellipse long axis. For each seed point, we generate a large oval as much as possible.
We found that the elliptic primitives obtained by the above calculation process are very large. In order to
use as few primitive bodies as possible to generate objects, the greedy algorithm is used to determine the final
set of effective elliptical primitives from all the candidate elliptical primitives. Starting from the elliptical
primitive with the largest contribution to the object, we add it to the set of valid elliptical primitives, and then
we choose to add the elliptic primitive with the largest contribution to the uncovered region to the effective
elliptical primitive set. If there are multiple ellipses with the same contribution, we select the ellipse with the
smallest radius.
3.2. Constructing the Non-realistic Ball Graphic Intelligent Surface
After obtaining the original body of the non-realistic form line, it is necessary to set the information of the
third dimension to generate the three-dimensional shape. Without loss of generality, we assume that the user
interaction interface is x-y plane and the non-realistic form line is on the plane. In this plane, we use the circle or
ellipse as the original body to approach the two-dimensional contour. When we set these circles or ellipse in the
z-axis direction of the size and its related parameters, the spherical, ellipsoid or super-quadratic surface can be
generated. The original body corresponds to a non-realistic form of the ball, which can be mixed after the given
contour of the three-dimensional objects.
The equation of a standard superquadratic surface is as follows:
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xn yn zn


1
Ran Rbn Rcn
(10)
Ra , Rb , Rc were the size of the three axes. n is a positive real number. In our application, the stub of the
generated hyperquadr in the plane of the parallel interface is an ellipse, which is called a hyperelance. The
super-ellipsoidal non-real-shaped morphological spherical graphic surface is a super-ellipsoid shape. A standard
super-ellipsoidal equation is as follows：
x2 y 2 zn


1
(11)
Ra2 Rb2 Rcn
Ra and Rb in the approximation of the non-real sense lines have been identified. The user can determine
the values of n and Rc using the formula (3) as the kernel function of non photorealistic shape ball. By the
formula (7), we can get points in space to the relative distance of the I ellipsoidal original body the calculation
formula:
It is a kernel function of a non-realistic morphological sphere by the formula (7). We can use the formula
(3) to determine the value of n and the value and we can get the relative distance of the point in the space to the
i-th super-ellipsoidal primitive:
i2   ri cos   
2

Ri2,a  ri cos   

2

2
Ri,b
 ri cos   

nc
Rin,cc
(12)
Equation (6) and equation (12) are substituted into equation (3), and the calculated value is the field value
of the spatial point p in the potential field defined by the super-ellipsoidal primitive. For each super-ellipsoidal
primitive, 9 free variables  xci , yci , zci , Ri ,a , Ri,b , Ri,c ,n, ,  to adjust the shape of the super-ellipsoidal nonrealistic form of the ball in our modeling method. The non-realistic shape line approximation can get a better
estimate of the xci , yci , zci , Ri ,a , Ri,b , Ri,c , , variables. Non-realistic shape of the ball can be changed into the
value to adjust, as shown in Figure 3.
Figure 3. The hyperellipsoid by different Rc , n of values
4. EXPERIMENTAL RESULT
This paper presents a non-realistic morphological ball modeling method that relies on the non-realistic
form of the line, which creates a non-realistic morphological ball system by a non-realistic form of line to obtain
a three-dimensional model. For complex models, the non-realistic form of each component of the model is
created by its non-realistic morphological ball system for the Buga / subtraction operation. Since our algorithm
is used a super-ellipsoidal non-realistic morphological sphere representation method, Flat model, we implement
the modeling method on a notebook computer configured for the Intel Core Duo CPU T2450 2.0GHz CPU + 1G
RAM. Here are some examples of how the image is rendered by the grid model after rendering the graphical
smart surface polygon. The relevant statistical data is seen in Table 1.
Table 1. List for test data
Model
Figure 7(c)
Samples
number
on the
silhouette
95
Medial circular or
elliptical approximation
Type
Number
Circle
92
Time(s)
Time for medial Time for
Energy
circles and ellipses parameters
generation
optimization Total
0.016
0.109
0.125 0.031
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Figure 8(a)
Figure 8(b)
Figure 8(c)
Figure 9(a)
Figure 9(b)
Figure 10
Body
Tail
Right back leg
Figure 11
Left back leg
Right front leg
Left front leg
Figure 12
Board
Human model
95
95
95
110
110
188
93
25
62
60
55
51
122
152
Circle
Circle
Ellipse
Ellipse
Ellipse
Ellipse
Circle
Circle
Circle
Circle
Circle
Circle
Ellipse
Ellipse
40
62
39
41
61
48
67
43
80
76
64
62
34
111
0.016
0.031
0.016
0.063
3.75
0.095
0.031
0.062
0.062
0.078
0.188
0.235
0.3
0.344
0.094
0.016
0.063
0.063
0.046
0.047
0.219
0.532
0.1
0.11
0.21
0.3
4.1
0.44
0.109
0.016
0.078
0.07
0.047
0.062
0.25
0.6
0.044
0.032
0.032
0.048
0.04
0.037
0.033
0.033
0.032
0.039
0.036
0.042
0.009
0.019
The results in Figure 4 show the outcome of the dolphin model using the spherical non-realistic
morphological spherical surface and the ellipsoidal non-real-shaped spherical surface, respectively. The left
figure in Figure 4 (a) is a non-real part of the dolphin model. Figure 4 (b) is the result of the use of 62 circles on
the basis of the same non-realistic morphological line in Figure 4 (a). The result of the approximation is shown
in Figure 4 (c). The left graph of Figure 4 (a) is the result of approximation using 39 ellipses on the basis of the
circle approximation in Figure 4. In this example, the surface parameter is set to Ri ,c ≤0.4, n = 2. From the
model results in Figure 4, it can be seen that the use of ellipsoidal non-realistic morphological sphere model is
less smooth than the original body, but the surface is smoother. If the spherical non-photorealistic rendering can
be achieved similar to the ellipsoid non-realistic shape of the spherical surface approximation effect, about 62
rounds are near the non-realistic form line.
(a) The modeling results by using 40 ball shape
(b) The modeling results by 62 spheroidal metaballs
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(c) The modeling results by 39 ellipsoid metaballs
Figure 4. Comparison with the results of the modeling using the ball and the ellipsoid non-realistic
morphological ball model
Figure 5 shows the results of the elliptic approximation of the non-real-looking morphological lines
obtained by different elliptic generation algorithms and the final ellipsoidal non-realistic morphological sphere
model (surface parameter Ri ,c ≤0.4, n = 2). In the experimental results, we find that the effect of using the
model based on the original input point and the dependent axis algorithm is not much different, and the
algorithm relying on the central axis is much more efficient than the algorithm that relies on the original input
point. In Figure 5 (a), the ellipse generation algorithm of the axis generates 41 elliptical primitives, which takes
63ms. The elliptical generation algorithm of the sampling point in Figure 5 (b) generates 61 elliptical primitives,
which takes 3750ms. In the later modeling process, Figure 3 shows the construction results of the hand model,
in which there are 188 sampling points on the non-sensional morphological lines, using the algorithm that
depends on the central axis to generate 48 Elliptical, time-consuming 32ms. The parameters of the superellipsoidal non-realistic morphological sphere model are Ri ,c ≤0.3, n = 2.
(a) Generation Algorithm of ellipse based on axle wire
(b) Generation Algorithm of ellipse based on sampling point
Figure 5. The comparison with the results of the non-realistic shape ball model by different elliptic
generation algorithms to come near the non-realistic shape line
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Figure 6. The hand model built by the ellipsoidal non-realistic shape ball model
5. CONCLUSIONS
In this paper, this papers proposes a modeling method based on the non-real form and non-real-shaped
morphological spherical graphic surface. Firstly, the user's model is extracted from the interface or from an
image or the complex model component that is not real. Then, it uses the two-dimensional primitive body (circle
or ellipse) to come near the non-realistic form line. Finally, by each two-dimensional primitive body, the user
sets the third dimension in space information. The three-dimensional model of the non-realistic shape line is
optimized by constructing the three-dimensional original body of the non-realistic shape ball system, and then
the contour model approximates the three-dimensional model of the given non-realistic shape line. The use of
ellipses is near the non-realistic form line to reduce the number of primitive bodies and provide better
approximation accuracy. We give two elliptical representations that generate the non-realistic morphological
lines: One is based on the central axis of the circular representation of the algorithm according to the expansion
of the algorithm. The other is based on the nonsense form of the original data of the algorithm. In order to
generate the three-dimensional model, the super-quadratic surface is used as the original body to construct the
model, and the formula of the spatial point field is provided. In the actual modeling process, we adopt the superellipsoid non-realistic shape spherical graphic surface, graphic intelligent surfaces and hyperquadratic properties
and our method of modeling, to generate some flat and quasi-swept adult models.
ACKNOWLEDGMENTS
This paper is supported by 2015 Heilongjiang Province Art and Science Planning Project Youth Fund,
Project Number: 2015D085.
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