WO2016173260A1 - Method and apparatus for decomposing three-dimensional model based on generalized cylinders - Google Patents

Abstract

A method and apparatus for decomposing a three-dimensional model based on generalized cylinders, which relate to the technical field of three-dimensional models. The method comprises: constructing local generalized cylinders by means of sampling points on the surface of a three-dimensional model; integrating the local generalized cylinders to form an over-complete coverage set from non-local generalized cylinders, and further acquiring a plurality of accurate coverage sets from the over-complete coverage set; and determining, according to an accurate coverage set corresponding to a minimum value in the sums of generalized cylindricities, a three-dimensional model decomposition way, so as to decompose the three-dimensional model. The problem of difficulty in optimal decomposition of a three-dimensional model based on generalized cylinders in the current field of three-dimensional model decompositions can be solved.

Description

Three-dimensional model segmentation method and device based on generalized cylinder Technical field

The invention relates to the technical field of three-dimensional models, in particular to a three-dimensional model segmentation method and device based on a generalized cylinder.

Background technique

Currently, the segmentation of 3D models is one of the fundamental problems of graphics and computational geometry. It is widely used in various aspects of 3D geometry processing, such as mesh simplification, parameterization and texture mapping, interactive editing, geometric deformation, spline surfaces. Reconstruction, model approximation and compression, skeleton extraction and animation correspondence, model matching and retrieval, and more. A typical model segmentation algorithm refers to segmenting a mesh model into a finite number of sub-grids that are connected and have a certain simple shape meaning, such as convex decomposition, according to certain geometric or topological features. Each sub-block constitutes an (approximate) convex polyhedron.

Generalized cylinders are a very common geometric primitive. For example, human, animal torso and limbs are all generalized cylinders. A generalized cylinder can be defined by a three-dimensional curve central axis, a curve skeleton, and a cross-section perpendicular to the skeleton. The generalized cylindrical three-dimensional entity has many functions, is easy to process, and can express a lot of shapes. Artificial crafts usually consist of many generalized cylinders. Compared with other simple primitives such as convex, the segmentation based on generalized cylinder can obtain more compact and more compact model segmentation.

However, although the generalized cylindrical shape is widely existed and has been successfully applied in skeleton extraction and modeling, it is difficult to optimize the segmentation of the 3D model based on the generalized cylinder in the field of 3D model segmentation.

Summary of the invention

Embodiments of the present invention provide a three-dimensional model segmentation method and apparatus based on a generalized cylinder to solve the problem that it is difficult to optimize segmentation of a three-dimensional model based on a generalized cylinder in the field of current three-dimensional model segmentation.

In order to achieve the above object, the present invention adopts the following technical solutions:

A three-dimensional model segmentation method based on generalized cylinders, including:

Obtaining a three-dimensional model, uniformly sampling the surface of the three-dimensional model by a standard Poisson disk sampling method, and acquiring a plurality of sampling points;

Constructing a plurality of local generalized cylinders by each of the plurality of sampling points;

The plurality of local generalized cylinders are subjected to fusion processing to form a plurality of non-local generalized cylinders; the plurality of non-local generalized cylinders constitute a candidate generalized cylindrical set; and the candidate generalized cylindrical set overcompletely covers the three-dimensional The surface of the model forms an overcomplete set of covers;

Acquiring a plurality of precise coverage sets from the overcomplete coverage set; wherein the precision coverage set comprises a plurality of generalized cylindrical components that do not overlap each other, and surface composition of the plurality of non-overlapping generalized cylindrical components The surface of the three-dimensional model;

Calculating a sum of generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets; the generalized cylindricity consisting of the flatness and the degree of profile change of the generalized cylindrical component;

Sorting the sum of the generalized cylines to determine the minimum of the sum of the generalized cylines;

Determining a three-dimensional model segmentation manner according to an exact coverage set corresponding to the minimum of the sum of the generalized cylines;

The three-dimensional model is segmented according to the three-dimensional model segmentation method.

Specifically, the constructing a plurality of local generalized cylinders by each of the plurality of sampling points comprises:

Determining a plurality of initial planes passing through the sampling point according to a sampling point;

Determining one or more aspects of the sampling point according to the plurality of initial planes;

Determining a center point of the intersection of the cut surface and the surface of the three-dimensional model, wherein the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cut surface is a rotation symmetry axis corresponding to the sampling point ;

Skeleton points corresponding to each two adjacent sampling points are connected along the rotational symmetry axis to form a central axis;

A profile curve on the surface of the three-dimensional model is uniformly sampled according to the central axis to form a partial generalized cylinder.

Specifically, the plurality of local generalized cylinders are subjected to fusion processing to form a plurality of non-local generalized cylinders, including:

Gradually merging adjacent local generalized cylinders to form a plurality of fused generalized cylinders;

If the generalized cylindricity of the fused generalized cylinder is smaller than the sum of the generalized cylines of the two local generalized cylinders before the fusion, the fusion generalized cylinder is determined to be a non-local generalized cylinder;

Separating overlapping regions of each non-local generalized cylinder to form a generalized cylindrical component that does not overlap each other;

The combination of the generally non-overlapping generalized cylindrical members is exhausted to form an updated generalized cylindrical member, and the updated generalized cylindrical member is used as a non-local generalized cylindrical body.

Specifically, the calculating a sum of generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets includes:

Calculate the generalized cylindricity GCity of each generalized cylindrical component:

GCity=E _s +αE _v

Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter.

In addition, the method for segmenting a three-dimensional model based on a generalized cylinder further includes:

Calculate the flatness E _s (n) of a generalized cylindrical part by the Douglas-Peucker algorithm:

Where C is a constant; n is the number of control points on the central axis fold line on the generalized cylindrical component; d _{i is} the approximation error corresponding to the i-th control point.

In addition, the method for segmenting a three-dimensional model based on a generalized cylinder further includes:

Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line;

Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set as the control point;

Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.

In addition, the method for segmenting a three-dimensional model based on a generalized cylinder further includes:

Calculate the profile change E _v (m) of a generalized cylindrical component by the Douglas-Peucker algorithm:

Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximation model according to the generalized cylindrical component; (f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.

In addition, the method for segmenting a three-dimensional model based on a generalized cylinder further includes:

Calculate the Hausdorff distance D(c _s , c _e ):

among them,

a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

Determining a maximum value among the first minimum distances;

Calculate the Hausdorff distance D(f _i ,f _i '):

among them,

To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

Representing a maximum of the respective second minimum distances.

In addition, the method for segmenting a three-dimensional model based on a generalized cylinder further includes:

Step 1. Perform linear interpolation on the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces;

Step 2: determining, on the generalized cylindrical component, a target profile curve having a maximum Hausdorff distance from a profile curve on the three-dimensional approximate model;

Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.

A three-dimensional model segmentation device based on a generalized cylinder, comprising:

a sampling unit, configured to acquire a three-dimensional model, and uniformly sample the surface of the three-dimensional model by a standard Poisson disk sampling method to obtain a plurality of sampling points;

a local generalized cylinder generating unit, configured to construct a plurality of local generalized cylinders by each of the plurality of sampling points;

a fusion unit for performing fusion processing on the plurality of local generalized cylinders to form a plurality of non-local generalized cylinders; the plurality of non-local generalized cylinders forming a candidate generalized cylindrical set; the candidate generalized cylindrical set Completely covering the surface of the three-dimensional model to form an over-complete coverage set;

An accurate coverage set obtaining unit, configured to obtain a plurality of precise coverage sets from the overcomplete coverage set; wherein the precision coverage set includes a plurality of generalized cylindrical components that do not overlap each other, and the plurality of mutually overlapping ones do not overlap each other The surface of the generalized cylindrical component constitutes the surface of the three-dimensional model;

a three-dimensional model segmentation mode determining unit, configured to calculate a sum of generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets; and to sort the sums of the generalized cylines to determine a minimum of sums of the generalized cylines a method for determining a three-dimensional model segmentation manner according to an exact cover set corresponding to a minimum value of the sum of the generalized cylines; the generalized cylindricity consisting of the flatness and the profile change degree of the generalized cylindrical component;

The three-dimensional model segmentation unit is configured to segment the three-dimensional model according to the three-dimensional model segmentation manner.

In addition, the local generalized cylinder generating unit is specifically configured to:

Determining a plurality of initial planes passing through the sampling point according to a sampling point;

Determining one or more aspects of the sampling point according to the plurality of initial planes;

Determining a center point of the intersection of the cut surface and the surface of the three-dimensional model, wherein the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cut surface is a rotation symmetry axis corresponding to the sampling point ;

Skeleton points corresponding to each two adjacent sampling points are connected along the rotational symmetry axis to form a central axis;

A profile curve on the surface of the three-dimensional model is uniformly sampled according to the central axis to form a partial generalized cylinder.

In addition, the fusion unit is specifically configured to:

Gradually merging adjacent local generalized cylinders to form a plurality of fused generalized cylinders;

If the generalized cylindricity of the fused generalized cylinder is smaller than the sum of the generalized cylines of the two local generalized cylinders before the fusion, the fusion generalized cylinder is determined to be a non-local generalized cylinder;

Separating overlapping regions of each non-local generalized cylinder to form a generalized cylindrical component that does not overlap each other;

The combination of the generally non-overlapping generalized cylindrical members is exhausted to form an updated generalized cylindrical member, and the updated generalized cylindrical member is used as a non-local generalized cylindrical body.

In addition, the three-dimensional model segmentation mode determining unit is specifically configured to:

Calculate the generalized cylindricity GCity of each generalized cylindrical component:

GCity=E _s +αE _v

Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter.

Further, the three-dimensional model segmentation device based on the generalized cylinder further includes:

A straightness calculation unit for calculating the flatness E _s (n) of a generalized cylindrical component by the Douglas-Peucker algorithm:

Where C is a constant; n is the number of control points on the central axis fold line on the generalized cylindrical component; d _{i is} the approximation error corresponding to the i-th control point.

Further, the three-dimensional model segmentation device based on the generalized cylinder further includes:

A central axis line modeling unit for performing:

Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line;

Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set as the control point;

Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.

Further, the three-dimensional model segmentation device based on the generalized cylinder further includes:

The profile change degree calculation unit is configured to calculate the profile change degree E _v (m) of the generalized cylindrical component by the Douglas-Peucker algorithm:

Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximation model according to the generalized cylindrical component; (f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.

In addition, the three-dimensional model segmentation device based on the generalized cylinder further includes:

The Hausdorff distance calculation unit is used to calculate the Hausdorff distance D(c _s , c _e ):

among them,

a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

Determining a maximum value among the first minimum distances;

The Hausdorff distance calculation unit is also used to calculate the Hausdorff distance D(f _i ,f _i '):

among them,

To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

Representing a maximum of the respective second minimum distances.

Further, the three-dimensional model segmentation device based on the generalized cylinder further includes:

A three-dimensional approximate model modeling unit for performing:

Step 1. Perform linear interpolation on the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces;

Step 2: determining, on the generalized cylindrical component, a target profile curve having a maximum Hausdorff distance from a profile curve on the three-dimensional approximate model;

Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.

The method and device for segmenting a three-dimensional model based on a generalized cylinder provided by an embodiment of the present invention constructs a local generalized cylinder through sampling points on the surface of the three-dimensional model, and then fuses the local generalized cylinder to form a non-local generalized cylinder. The overcomplete coverage set, and then obtains multiple precise coverage sets from the overcomplete coverage set, and determines a three-dimensional model segmentation method according to the precise coverage set corresponding to the minimum of the generalized cylindricity, thereby performing three-dimensional model segmentation. It can be seen that the present invention can determine a globally optimal three-dimensional model segmentation method by the above manner, and solves the problem that it is difficult to optimize segmentation of the three-dimensional model based on the generalized cylinder in the current three-dimensional model segmentation field.

DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below. Obviously, the drawings in the following description are only It is a certain embodiment of the present invention, and other drawings can be obtained from those skilled in the art without any inventive labor.

1 is a flow chart 1 of a method for segmenting a three-dimensional model based on a generalized cylinder according to an embodiment of the present invention;

2 is a flow chart 2 of a method for segmenting a three-dimensional model based on a generalized cylinder according to an embodiment of the present invention;

3 is a schematic diagram of generating a central axis fold line and a control point according to an embodiment of the present invention;

4 is a schematic diagram of generating a three-dimensional approximate model and a cross-sectional curve on a three-dimensional approximate model in an embodiment of the present invention;

FIG. 5 is a schematic structural diagram 1 of a three-dimensional model segmentation apparatus based on a generalized cylinder according to an embodiment of the present invention; FIG.

FIG. 6 is a schematic structural diagram 2 of a three-dimensional model segmentation apparatus based on a generalized cylinder according to an embodiment of the present invention.

detailed description

The technical solutions in the embodiments of the present invention are clearly and completely described in the following with reference to the accompanying drawings in the embodiments of the present invention. It is obvious that the described embodiments are only a part of the embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

As shown in FIG. 1 , an embodiment of the present invention provides a three-dimensional model segmentation method based on a generalized cylinder, including:

Step 101: Acquire a three-dimensional model, and uniformly sample the surface of the three-dimensional model by a standard Poisson disk sampling method to obtain a plurality of sampling points.

Step 102: Construct a plurality of local generalized cylinders by each of the plurality of sampling points.

Step 103: Perform fusion processing on the plurality of local generalized cylinders to form a plurality of non-local generalized cylinders.

The plurality of non-local generalized cylinders constitute a candidate generalized cylinder set; the candidate generalized cylindrical set overcompletely covers the surface of the three-dimensional model to form an over-complete coverage set.

Step 104: Acquire a plurality of precise coverage sets from the overcomplete coverage set.

Wherein, an accurate cover set includes a plurality of generalized cylindrical members that do not overlap each other, and surfaces of the plurality of non-overlapping generalized cylindrical members constitute a surface of the three-dimensional model.

Step 105: Calculate the sum of the generalized cylines of each generalized cylindrical component in each precise coverage set.

Wherein, the generalized cylindricity consists of the flatness and the degree of profile change of the generalized cylindrical component.

Step 106: Sort the sum of the generalized cylines to determine the minimum of the sum of the generalized cylines.

Step 107: Determine a three-dimensional model segmentation manner according to an accurate coverage set corresponding to a minimum value of sums of the generalized cylines.

Step 108: Segment the three-dimensional model according to the three-dimensional model segmentation manner.

The three-dimensional model segmentation method based on generalized cylinder provided by the embodiment of the present invention constructs a local generalized cylinder by sampling points on the surface of the three-dimensional model, and then fuses the local generalized cylinder to form a non-local generalized cylinder. A complete coverage set is obtained, and a plurality of precise coverage sets are obtained from the overcomplete coverage set, and a three-dimensional model segmentation mode is determined according to an accurate coverage set corresponding to the minimum value of the sum of the generalized cylindrimen, thereby performing three-dimensional model segmentation. It can be seen that the present invention can determine a globally optimal three-dimensional model segmentation method by the above manner, and solves the problem that it is difficult to optimize segmentation of the three-dimensional model based on the generalized cylinder in the current three-dimensional model segmentation field.

In order to make the present invention better understood by those skilled in the art, a more detailed embodiment is shown below. As shown in FIG. 2, the embodiment of the present invention provides a three-dimensional model segmentation method based on a generalized cylinder, including:

Step 201: Acquire a three-dimensional model, and uniformly sample the surface of the three-dimensional model by a standard Poisson disk sampling method to obtain a plurality of sampling points.

Step 202: Determine, according to a sampling point, a plurality of initial planes passing through the sampling point.

Steps 202 to 206 are performed using a Rotational Symmetry Axis (ROSA) technique. The plurality of initial planes may be N, and N is generally 24.

Step 203: Determine one or more aspects of the sampling point according to the plurality of initial planes.

For each initial plane, according to the normal vector distribution on the intersection with the surface of the three-dimensional model, a new plane can be calculated, and then iterated until the plane no longer changes, this plane is called the cutting plane of the point (Cutting Plane); For cylindrical regions, generally all initial planes eventually converge to the same slice, while for non-columnar regions, there may be multiple slices.

Step 204: Determine a center point of a line of intersection between the cut surface and a surface of the three-dimensional model, where the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cut surface is corresponding to the sampling point. Rotational symmetry axis.

Step 205: Connect the skeleton points corresponding to each two adjacent sampling points along the rotational symmetry axis to form a central axis.

Step 206: Evenly sampling a profile curve on a surface of the three-dimensional model according to the central axis to form a partial generalized cylinder.

Step 207, gradually merging the adjacent local generalized cylinders to form a plurality of fused generalized cylinders.

Since the local generalized cylinder is constructed in the neighborhood of the sampling point, there is a large amount of overlap. Although it constitutes an over-complete coverage of the surface of the three-dimensional model, this does not guarantee the existence of an accurate coverage set. In order to reduce the scale of the segmentation and obtain the least number of generalized cylindrical segments, the local generalized cylinders need to be fused here.

Step 208: If the generalized cylindricity of the fused generalized cylinder is smaller than the sum of the generalized cylines of the two local generalized cylinders before the fusion, the fused generalized cylinder is determined to be a non-local generalized cylinder.

Its formula is expressed as:

GCity(A⊕B)<GCity(A)+GCity(B)

Among them, GCity(A) is the generalized cylindricity of A generalized cylinder, GCity(B) is the generalized cylindricity of B generalized cylinder, and GCity(A⊕B) is the generalized cylinder of generalized cylinder with A and B fusion degree. For the calculation method of the generalized cylindricity, refer to the subsequent step 212, which will not be repeated here.

Step 209: Separating overlapping regions of each non-local generalized cylinder to form a generalized cylindrical component that does not overlap each other.

Step 210: Extending the combination of the non-overlapping generalized cylindrical members to form an updated generalized cylindrical member, and using the updated generalized cylindrical member as a non-local generalized cylindrical body.

It is worth noting that these non-overlapping generalized cylindrical components can be used as building blocks, and all possible generalized cylindrical components can be constructed by exhausting brick combinations. In this way, it can be guaranteed There must be an exact set of coverage in the over-complete coverage set, and it is also possible to construct new generalized cylindrical parts that cannot be constructed by merging local generalized cylinders.

The plurality of non-local generalized cylinders constitute a candidate generalized cylinder set; the candidate generalized cylindrical set overcompletely covers the surface of the three-dimensional model to form an over-complete coverage set.

Step 211: Acquire a plurality of precise coverage sets from the overcomplete coverage set.

Wherein, an accurate cover set includes a plurality of generalized cylindrical members that do not overlap each other, and surfaces of the plurality of non-overlapping generalized cylindrical members constitute a surface of the three-dimensional model.

In step 211, the Algorithm X algorithm can be used to quickly enumerate all valid precision coverage sets from a set of overcomplete coverage sets.

Step 212: Calculate the sum of the generalized cylines of each of the generalized cylindrical components in each precise coverage set.

Among them, the calculation of the generalized cylindricity GCity of each generalized cylindrical component can be realized by the following formula:

GCity=E _s +αE _v

Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter, and α is generally 1.

For the flatness described above, the flatness E _s (n) of the generalized cylindrical part can be calculated by the Douglas-Peucker algorithm:

Where C is a constant, when the C value becomes larger, it will stimulate the long axis of the long polyline; on the contrary, when the C value becomes smaller, the excitation will divide the middle axis into many shorter polylines; n is the middle of the generalized cylindrical part. The number of control points on the axis fold line; the approximation error corresponding to the i-th control point of d _i .

For the above-mentioned central axis fold line and control point, it can be generated by the following three steps, for example, a three-dimensional model of a gecko shape as shown in FIG. 3, the head-to-tail curve can be used as a central axis curve for the central axis curve , you can generate the axis polyline and the control point:

Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line.

Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set to the control point.

For example, in Fig. 3, P ₁ , P ₂ , P _{3 ,} ... P ₁₁ are the above-mentioned target points, and d ₁ , d ₂ , and d ₃ are the distances of P ₁ , P ₂ , and P ₃ from the central axis line, respectively. Here, it should be noted that the central axis fold line does not remain unchanged all the time, but is continuously updated by the following step 3. The resulting central axis fold line is close to the central axis curve.

Additionally, the first distance threshold can generally be 0.005.

Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.

For example, if P ₁ is the target point farthest from the straight line p _s p _e , and the distance is greater than the first distance threshold, then the central axis line is re-determined as p _s p ₁ p _e , and then step 2 is performed to obtain the control point P. ₂ , re-determining the central axis line as p _s p ₂ p ₁ p _e , in this way, the distance from the point on the central axis curve to the central axis line is less than or equal to the first distance threshold.

In addition, for the above-mentioned profile change degree, the profile change degree E _v (m) of the generalized cylindrical component can be calculated by the Douglas-Peucker algorithm:

Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximate model of the generalized cylindrical component; D( f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.

For the above Hausdorff distance, it can be calculated as follows:

For example, calculate the Hausdorff distance D(c _s , c _e ):

among them,

a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

Representing a maximum value among the first minimum distances.

Another example is to calculate the Hausdorff distance D(f _i ,f _i '):

among them,

To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

Representing a maximum of the respective second minimum distances.

In addition, for the above three-dimensional approximation model and the profile curve on the three-dimensional approximation model (the profile curve corresponding to the formation of the control profile surface), it can be generated by the following three steps, for example, a three-dimensional model as shown in FIG. 4, and a three-dimensional approximate model thereof The generation and control of the profile surface is generated as follows:

Step 1. Linearly interpolating the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces.

Step 2. Determine a target profile curve having the largest Hausdorff distance from the profile curve on the three-dimensional approximation model on the generalized cylindrical component.

For example, in FIG. 4, f ₁ to f ₈ are respectively eight target section curves, and the eight target section curves constitute eight control section curved surfaces. It is worth noting that the three-dimensional approximation model is not always the same, but is continuously updated by the following step 3. The resulting three-dimensional approximation model is close to the generalized cylindrical component.

Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.

For example, when the cross-sectional curves c _s and c _e are linearly interpolated to generate a three-dimensional approximation model, a target profile curve having the largest Hausdorff distance from the profile curve f ₁ ' on the three-dimensional approximation model is determined on the generalized cylindrical component. f ₁ , and the Hausdorff distance is greater than a second distance threshold, then re-determining a three-dimensional approximation model according to the profile curves c _s , c _e and f ₁ , and then continuing to perform the above step 2, in this way, obtaining a subsequent target profile The curve until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.

Step 213: Sort the sum of the generalized cylines to determine the minimum of the sum of the generalized cylines.

Step 214: Determine a three-dimensional model segmentation manner according to an accurate coverage set corresponding to a minimum value of sums of the generalized cylines.

Step 215: Segment the three-dimensional model according to the three-dimensional model segmentation manner.

The three-dimensional model segmentation method based on generalized cylinder provided by the embodiment of the present invention constructs a local generalized cylinder by sampling points on the surface of the three-dimensional model, and then fuses the local generalized cylinder to form a non-local generalized cylinder. A complete coverage set is obtained, and a plurality of precise coverage sets are obtained from the overcomplete coverage set, and a three-dimensional model segmentation mode is determined according to an accurate coverage set corresponding to the minimum value of the sum of the generalized cylindrimen, thereby performing three-dimensional model segmentation. It can be seen that the present invention can determine a globally optimal three-dimensional model segmentation method by the above manner, and solves the problem that it is difficult to optimize segmentation of the three-dimensional model based on the generalized cylinder in the current three-dimensional model segmentation field.

Corresponding to the foregoing method embodiment, as shown in FIG. 5, an embodiment of the present invention provides a three-dimensional model segmentation device based on a generalized cylinder, including:

The sampling unit 31 can acquire a three-dimensional model and uniformly sample the surface of the three-dimensional model by a standard Poisson disk sampling method to acquire a plurality of sampling points.

The local generalized cylinder generating unit 32 can construct a plurality of local generalized cylinders through each of the plurality of sampling points.

The fusion unit 33 may perform fusion processing on a plurality of local generalized cylinders to form a plurality of non-local generalized cylinders; the plurality of non-local generalized cylinders constitute a candidate generalized cylinder set; the candidate generalized cylindrical set overcompletely covers the The surface of the 3D model forms an overcomplete set of covers.

The precise coverage set obtaining unit 34 may obtain a plurality of precise coverage sets from the overcomplete coverage set; wherein the precision coverage set includes a plurality of generalized cylindrical components that do not overlap each other, and the plurality of non-overlapping generalized The surface of the cylindrical component constitutes the surface of the three-dimensional model.

The three-dimensional model segmentation mode determining unit 35 may calculate the sum of the generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets; sort the sum of the generalized cylines to determine the minimum of the sum of the generalized cylines a value; a three-dimensional model segmentation manner is determined according to the precise coverage set corresponding to the minimum of the sum of the generalized cylines; the generalized cylindricity is composed of the flatness and the profile change degree of the generalized cylindrical component.

The three-dimensional model segmentation unit 36 can segment the three-dimensional model according to the three-dimensional model segmentation method.

In addition, the local generalized cylinder generating unit 32 may specifically:

Determining, according to a sampling point, a plurality of initial planes passing through the sampling point, and determining one or more aspects of the sampling point according to the plurality of initial planes; determining a line of intersection of the section with the surface of the three-dimensional model a center point, wherein the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cutting plane is a rotation symmetry axis corresponding to the sampling point; and a skeleton point corresponding to each two adjacent sampling points is along The rotational symmetry axes are connected to form a central axis; the profile curve on the surface of the three-dimensional model is uniformly sampled according to the central axis to form a partial generalized cylinder.

In addition, the fusion unit 33 can specifically fuse adjacent local generalized cylinders to form a plurality of fused generalized cylinders; if the generalized cylindricity of the fused generalized cylinder is smaller than two local generalized before fusion The sum of the generalized cylines of the cylinder determines that the fused generalized cylinder is a non-local generalized cylinder; the overlapping regions of the non-local generalized cylinders are separated to form a generalized cylindrical component that does not overlap each other; The combination of the generalized cylindrical members that do not overlap each other forms an updated generalized cylindrical member, and the updated generalized cylindrical member is regarded as a non-local generalized cylindrical body.

In addition, the three-dimensional model segmentation manner determining unit 35 may specifically:

Calculate the generalized cylindricity GCity of each generalized cylindrical component:

GCity=E _s +αE _v

Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter.

Further, as shown in FIG. 6, the three-dimensional model segmentation device based on the generalized cylinder may further include:

The flatness calculation unit 37 can calculate the flatness E _s (n) of the generalized cylindrical member by the Douglas-Peucker algorithm:

Where C is a constant; n is the number of control points on the central axis fold line on the generalized cylindrical component; d _{i is} the approximation error corresponding to the i-th control point.

Further, as shown in FIG. 6, the three-dimensional model segmentation device based on the generalized cylinder may further include:

A central axis polyline modeling unit 38, which can execute:

Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line.

Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set to the control point.

Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.

Further, as shown in FIG. 6, the three-dimensional model segmentation device based on the generalized cylinder further includes:

The profile change degree calculation unit 39 can calculate the profile change degree E _v (m) of the generalized cylindrical component by the Douglas-Peucker algorithm:

Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximation model according to the generalized cylindrical component; (f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.

In addition, as shown in FIG. 6, the three-dimensional model segmentation apparatus based on the generalized cylinder may further include:

The Hausdorff distance calculation unit 40 can calculate the Hausdorff distance D(c _s , c _e ):

among them,

a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

Representing a maximum value among the first minimum distances.

The Hausdorff distance calculation unit 40 can also calculate the Hausdorff distance D(f _i ,f _i ):

among them,

To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

Representing a maximum of the respective second minimum distances.

Further, as shown in FIG. 6, the three-dimensional model segmentation device based on the generalized cylinder may further include:

The three-dimensional approximate model modeling unit 41 can execute:

Step 1. Linearly interpolating the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces.

Step 2. Determine a target profile curve having the largest Hausdorff distance from the profile curve on the three-dimensional approximation model on the generalized cylindrical component.

Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.

It should be noted that the specific implementation manner of the three-dimensional model segmentation device based on the generalized cylinder provided by the embodiment of the present invention can be referred to the method embodiment shown in FIG. 1 and FIG. 2, and details are not described herein again.

The three-dimensional model segmentation device based on the generalized cylinder provided by the embodiment of the present invention constructs a local generalized cylinder through the sampling points on the surface of the three-dimensional model, and then fuses the local generalized cylinder to form a non-local generalized cylinder. A complete coverage set is obtained, and a plurality of precise coverage sets are obtained from the overcomplete coverage set, and a three-dimensional model segmentation mode is determined according to an accurate coverage set corresponding to the minimum value of the sum of the generalized cylindrimen, thereby performing three-dimensional model segmentation. It can be seen that the present invention can determine a global optimal three-dimensional model segmentation method by the above manner, and convert the model segmentation problem into a surface accurate cover problem, which can ensure that the final segmentation converges to a minimum number, and each component is sufficiently simple to segment. . It solves the problem that it is difficult to optimize segmentation of 3D models based on generalized cylinders in the current 3D model segmentation field.

Those skilled in the art will appreciate that embodiments of the present invention can be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or a combination of software and hardware. Moreover, the invention can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) including computer usable program code.

The present invention has been described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (system), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or FIG. These computers are available Program instructions to a processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that instructions executed by a processor of a computer or other programmable data processing device are generated for implementation in a process A device or a plurality of processes and/or block diagrams of a device in a block or a plurality of blocks.

The computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture comprising the instruction device. The apparatus implements the functions specified in one or more blocks of a flow or a flow and/or block diagram of the flowchart.

These computer program instructions can also be loaded onto a computer or other programmable data processing device such that a series of operational steps are performed on a computer or other programmable device to produce computer-implemented processing for execution on a computer or other programmable device. The instructions provide steps for implementing the functions specified in one or more of the flow or in a block or blocks of a flow diagram.

The principles and embodiments of the present invention have been described in connection with the specific embodiments of the present invention. The description of the above embodiments is only for the understanding of the method of the present invention and the core idea thereof. At the same time, for those skilled in the art, according to the present invention The present invention is not limited by the scope of the present invention.

Claims (18)

1. A three-dimensional model segmentation method based on generalized cylinders, comprising:

   Obtaining a three-dimensional model, uniformly sampling the surface of the three-dimensional model by a standard Poisson disk sampling method, and acquiring a plurality of sampling points;

   Constructing a plurality of local generalized cylinders by each of the plurality of sampling points;

   The plurality of local generalized cylinders are subjected to fusion processing to form a plurality of non-local generalized cylinders; the plurality of non-local generalized cylinders constitute a candidate generalized cylindrical set; and the candidate generalized cylindrical set overcompletely covers the three-dimensional The surface of the model forms an overcomplete set of covers;

   Acquiring a plurality of precise coverage sets from the overcomplete coverage set; wherein the precision coverage set comprises a plurality of generalized cylindrical components that do not overlap each other, and surface composition of the plurality of non-overlapping generalized cylindrical components The surface of the three-dimensional model;

   Calculating a sum of generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets; the generalized cylindricity consisting of the flatness and the degree of profile change of the generalized cylindrical component;

   Sorting the sum of the generalized cylines to determine the minimum of the sum of the generalized cylines;

   Determining a three-dimensional model segmentation manner according to an exact coverage set corresponding to the minimum of the sum of the generalized cylines;

   The three-dimensional model is segmented according to the three-dimensional model segmentation method.
2. The method for segmenting a three-dimensional model based on a generalized cylinder according to claim 1, wherein the constructing a plurality of local generalized cylinders by each of the plurality of sampling points comprises:

   Determining a plurality of initial planes passing through the sampling point according to a sampling point;

   Determining one or more aspects of the sampling point according to the plurality of initial planes;

   Determining a center point of the intersection of the cut surface and the surface of the three-dimensional model, wherein the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cut surface is a rotation symmetry axis corresponding to the sampling point ;

   Skeleton points corresponding to each two adjacent sampling points are connected along the rotational symmetry axis to form a central axis;

   A profile curve on the surface of the three-dimensional model is uniformly sampled according to the central axis to form a partial generalized cylinder.
3. The method for segmenting a three-dimensional model based on a generalized cylinder according to claim 1, wherein the plurality of local generalized cylinders are fused to form a plurality of non-local generalized cylinders, including:

   Gradually merging adjacent local generalized cylinders to form a plurality of fused generalized cylinders;

   If the generalized cylindricity of the fused generalized cylinder is smaller than the sum of the generalized cylines of the two local generalized cylinders before the fusion, the fusion generalized cylinder is determined to be a non-local generalized cylinder;

   Separating overlapping regions of each non-local generalized cylinder to form a generalized cylindrical component that does not overlap each other;

   The combination of the generally non-overlapping generalized cylindrical members is exhausted to form an updated generalized cylindrical member, and the updated generalized cylindrical member is used as a non-local generalized cylindrical body.
4. The generalized cylinder-based three-dimensional model segmentation method according to claim 3, wherein said calculating a sum of generalized cylines of each of the generalized cylindrical members in each of said precise coverage sets comprises:

   Calculate the generalized cylindricity GCity of each generalized cylindrical component:

   GCity=E _s +αE _v

   Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter.
5. The method of claim 3, wherein the method further comprises:

   Calculate the flatness E _s (n) of a generalized cylindrical part by the Douglas-Peucker algorithm:

   

   Where C is a constant; n is the number of control points on the central axis fold line on the generalized cylindrical component; d _{i is} the approximation error corresponding to the i-th control point.
6. The method of claim 3, wherein the method further comprises:

   Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line;

   Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set as the control point;

   Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.
7. The method of claim 3, wherein the method further comprises:

   Calculate the profile change E _v (m) of a generalized cylindrical component by the Douglas-Peucker algorithm:

   

   Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximation model according to the generalized cylindrical component; (f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.
8. The method of claim 3, wherein the method further comprises:

   Calculate the Hausdorff distance D(c _s , c _e ):

   

   among them,

   

   a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

   

   Determining a maximum value among the first minimum distances;

   Calculate the Hausdorff distance D(f _i ,f _i '):

   

   among them,

   

   To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

   

   Representing a maximum of the respective second minimum distances.
9. The method for segmenting a three-dimensional model based on a generalized cylinder according to claim 8, further comprising:

   Step 1. Perform linear interpolation on the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces;

   Step 2: determining, on the generalized cylindrical component, a target profile curve having a maximum Hausdorff distance from a profile curve on the three-dimensional approximate model;

   Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the Hausdorff distance of the profile curve on the generalized cylindrical component and the profile curve on the three-dimensional approximation model is less than or equal to the second distance threshold.
10. A three-dimensional model segmentation device based on a generalized cylinder, comprising:

    a sampling unit, configured to acquire a three-dimensional model, and uniformly sample the surface of the three-dimensional model by a standard Poisson disk sampling method to obtain a plurality of sampling points;

    a local generalized cylinder generating unit, configured to construct a plurality of local generalized cylinders by each of the plurality of sampling points;

    a fusion unit for performing fusion processing on the plurality of local generalized cylinders to form a plurality of non-local generalized cylinders; the plurality of non-local generalized cylinders forming a candidate generalized cylindrical set; the candidate generalized cylindrical set Completely covering the surface of the three-dimensional model to form an over-complete coverage set;

    An accurate coverage set obtaining unit, configured to obtain a plurality of precise coverage sets from the overcomplete coverage set; wherein the precision coverage set includes a plurality of generalized cylindrical components that do not overlap each other, and the plurality of mutually overlapping ones do not overlap each other The surface of the generalized cylindrical component constitutes the surface of the three-dimensional model;

    a three-dimensional model segmentation mode determining unit, configured to calculate a sum of generalized cylines of each of the generalized cylindrical components in each of the precise coverage sets; and to sort the sums of the generalized cylines to determine a minimum of sums of the generalized cylines a method for determining a three-dimensional model segmentation manner according to an exact cover set corresponding to a minimum value of the sum of the generalized cylines; the generalized cylindricity consisting of the flatness and the profile change degree of the generalized cylindrical component;

    The three-dimensional model segmentation unit is configured to segment the three-dimensional model according to the three-dimensional model segmentation manner.
11. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 10, wherein the local generalized cylinder generating unit is specifically configured to:

    Determining a plurality of initial planes passing through the sampling point according to a sampling point;

    Determining one or more aspects of the sampling point according to the plurality of initial planes;

    Determining a center point of the intersection of the cut surface and the surface of the three-dimensional model, wherein the center point is used as a skeleton point corresponding to the sampling point, and a normal vector of the cut surface is a rotation symmetry axis corresponding to the sampling point ;

    Skeleton points corresponding to each two adjacent sampling points are connected along the rotational symmetry axis to form a central axis;

    A profile curve on the surface of the three-dimensional model is uniformly sampled according to the central axis to form a partial generalized cylinder.
12. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 10, wherein the fusion unit is specifically configured to:

    Gradually merging adjacent local generalized cylinders to form a plurality of fused generalized cylinders;

    If the generalized cylindricity of the fused generalized cylinder is smaller than the sum of the generalized cylines of the two local generalized cylinders before the fusion, the fusion generalized cylinder is determined to be a non-local generalized cylinder;

    Separating overlapping regions of each non-local generalized cylinder to form a generalized cylindrical component that does not overlap each other;

    The combination of the generally non-overlapping generalized cylindrical members is exhausted to form an updated generalized cylindrical member, and the updated generalized cylindrical member is used as a non-local generalized cylindrical body.
13. The apparatus for determining a three-dimensional model based on a generalized cylinder according to claim 12, wherein the three-dimensional model segmentation mode determining unit is specifically configured to:

    Calculate the generalized cylindricity GCity of each generalized cylindrical component:

    GCity=E _s +αE _v

    Where E _s is the flatness; E _v is the degree of change of the profile; α is a weight parameter.
14. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 13, further comprising:

    A straightness calculation unit for calculating the flatness E _s (n) of a generalized cylindrical component by the Douglas-Peucker algorithm:

    

    Where C is a constant; n is the number of control points on the central axis fold line on the generalized cylindrical component; d _{i is} the approximation error corresponding to the i-th control point.
15. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 14, further comprising:

    A central axis line modeling unit for performing:

    Step 1. Determine a straight line p _s p _e according to the two end points p _s and p _e of the central axis curve of the generalized cylindrical component, and use the straight line p _s p _e as the central axis fold line;

    Step 2: determining a target point having the largest distance from the central axis line on the central axis curve, and if the distance between the target point and the central axis line is greater than a first distance threshold, the target point is Set as the control point;

    Step 3: Redetermining a central axis line according to the control point, and returning to step 2 until the distance between the point on the central axis curve and the central axis line is less than or equal to the first distance threshold; The distance between the point on the central axis curve and the central axis line is the approximation error.
16. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 13, further comprising:

    The profile change degree calculation unit is configured to calculate the profile change degree E _v (m) of the generalized cylindrical component by the Douglas-Peucker algorithm:

    

    Where D(c _s , c _e ) is the Hausdorff distance of the profile curves c _s and c _e selected at both ends of the generalized cylindrical component; m is the number of profile curves on the three-dimensional approximation model according to the generalized cylindrical component; (f _i , f _i ') is the Hausdorff distance of the profile curve f _i on the generalized cylindrical component and a profile curve f _i ' on the three-dimensional approximation model of the generalized cylindrical component.
17. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 16, further comprising:

    The Hausdorff distance calculation unit is used to calculate the Hausdorff distance D(c _s , c _e ):

    

    among them,

    

    a first minimum distance from each point k on the profile curve c _s to each point h on the profile curve c _e ;

    

    Determining a maximum value among the first minimum distances;

    The Hausdorff distance calculation unit is also used to calculate the Hausdorff distance D(f _i ,f _i '):

    

    among them,

    

    To each point on the sectional curve k f _i f _i to the cross-sectional profile of each second minimum distance of each point on h '; the

    

    Representing a maximum of the respective second minimum distances.
18. The apparatus for dividing a three-dimensional model based on a generalized cylinder according to claim 17, further comprising:

    A three-dimensional approximate model modeling unit for performing:

    Step 1. Perform linear interpolation on the profile curves c _s and c _e selected at both ends of the generalized cylindrical component to generate a three-dimensional approximate model; the profile curves c _s and c _e respectively form two control profile surfaces;

    Step 2: determining, on the generalized cylindrical component, a target profile curve having a maximum Hausdorff distance from a profile curve on the three-dimensional approximate model;

    Step 3: If the Hausdorff distance of the target profile curve and the profile curve on the three-dimensional approximate model is greater than a second distance threshold, insert a face formed by the target profile curve into the control profile surface to reconstruct a three-dimensional shape. Approximating the model, returning to step 2 until the profile curve on the generalized cylindrical component and the three-dimensional

    The Hausdorff distance of the profile curve on the approximate model is less than or equal to the second distance threshold.

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