CN108648268B - Human body model approximation method based on capsule - Google Patents
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Abstract
The invention discloses a capsule-based human body model approximation method which comprises the following steps of (1) inputting a three-dimensional human body model, (2) extracting characteristic lines of the three-dimensional human body model input in the step (1), (3) approximating each characteristic line generated in the step (2) by using a plurality of circles, (4) generating balls according to the circles generated in the step (3), pairing every two balls on adjacent characteristic lines to generate capsules, and (5) automatically adjusting the sizes of the balls and the capsules to enable the human body model to be completely in an approximation body.
Description
Technical Field
The invention relates to the technical field of three-dimensional model approximation, in particular to a human body model approximation method based on capsules.
Background
The method for approximating the complex three-dimensional model by using the simple geometric elements has high application value in computer graphics, particularly applications with high time requirements, such as shape analysis, collision detection, shadow generation, occlusion rejection and the like. Common geometric elements include, spheres, ellipsoids, Axis Aligned Bounding Boxes (AABB), Oriented Bounding Boxes (OBB), discrete oriented polyhedrons (k-DOP), and the like. Of these geometric elements, the sphere is the simplest and therefore widely used in computer graphics applications. Capsules consisting of two balls are often used to approximate mannequins for real-time cloth simulation, such as open source physics engine bullets and PhysX, because of their simplicity and efficiency in collision detection. However, the capsule approximation body of the three-dimensional human body model is still generated manually at present, and is time-consuming and labor-consuming.
More recently, Thiery et al have proposed Sphere-sheets, i.e., shapes interpolated along edges and triangles of a Sphere (see Thiery, J.M., Guy, E., Boubekeur, T.: Sphere-sheets: Shape approximation using a spherical geometric error methodology, ACM trans. graph.32(6),178 (2013)). The method has the advantages that various types of three-dimensional models including human bodies, animals and the like can be processed, the method has the defect that when the number of the balls is small (less than 300), the approximation error is large, and for a symmetrical human body model, the approximation body generated by the method cannot guarantee the symmetry. On the other hand, the interpolation of the Sphere along the edges can be regarded as a capsule, and the interpolation of the Sphere along the triangle is actually three capsules (one for each edge) and two external tangent planes (the external tangent planes of the three spheres), that is, the approximation generated by Sphere-Meshes also contains the triangular plane and cannot be directly applied to bullets or PhysX.
Therefore, it is necessary to automatically and rapidly generate a capsule approximation body of the three-dimensional human body model.
Patent document No. CN106971420A discloses a three-dimensional personalized human body modeling method based on features, which comprises the following steps: 1) according to the biological principle, the human body characteristics are locally partitioned; 2) extracting characteristic points of each human body block, analyzing the incidence relation of the characteristic points, and constructing a characteristic point set and a characteristic relation set of the whole human body; 3) fitting the characteristic points of each human body block by using a B-spline curve to obtain a three-dimensional human body model with a plurality of characteristic curves; 4) and processing the three-dimensional human body model with the plurality of characteristic curves by adopting an interpolation method to obtain a final three-dimensional human body model. The invention provides an efficient and accurate implementation technology, which is used for improving the speed and the accuracy of three-dimensional personalized human body construction and higher user satisfaction, optimizing the human body characteristic point selection efficiency, improving the characteristic analysis precision and constructing a three-dimensional personalized human body model closest to a real person.
Disclosure of Invention
The invention aims to provide a capsule-based human body model approximation method. The capsule-based human model approximation method provided by the invention is simple, novel and quick, and can quickly generate a closer and more symmetrical human model approximation body for a given three-dimensional human model.
The invention provides the following technical scheme:
a capsule-based mannequin approximation method comprising the steps of:
(1) inputting a three-dimensional human body model;
(2) extracting the characteristic line of the three-dimensional human body model input in the step (1);
(3) approximating each of the characteristic lines generated in step (2) with a plurality of circles;
(4) generating balls according to the circles generated in the step (3); pairing the balls on the adjacent characteristic lines in pairs to generate capsules, and deleting the capsules completely positioned in other capsules;
(5) the sizes of the ball and the capsule are automatically adjusted, so that the human body model is completely positioned in the approaching body.
Further, the three-dimensional human body model in the step (1) can be represented by a triangular mesh or a quadrilateral mesh.
In the step (2), the characteristic line is a boundary line of a cross section of the body part near the joint point and is represented by a polygon.
Further, the characteristic lines include waist, shoulder, neck, elbow, wrist, knee and ankle characteristic lines.
Further, the extraction of the characteristic line can be performed by a manual method or an automatic method.
In the step (3), the approximation method using each characteristic line generated in the step (2) is an iterative L loyd clustering algorithm.
Wherein the number of circles is specified by the user.
The approximation error of the iterative L loyd clustering algorithm is the sum of the areas of the circles in the outer regions of the characteristic line, and is defined as follows:
wherein n iscRepresenting the number of circles used to approximate the characteristic line, E being the set of edges of the characteristic line, A (E, C)i) Represents the ith circle CiThe area outside the characteristic line is denoted as COA.
The area COA of the circle in the outer area of the characteristic line is calculated by adopting a side-by-side calculation method, and the k-th side EkLet p be0、p1Is EkAnd both located at CiInside, the area A (E) corresponding to the sidek，Ci) The calculation is as follows:
A(Ek，Ci)＝Asec(Ek，Ci)-Atri(Ek，oi)
wherein A issec(Ek，Ci) Is a circle CiCenter o of circleiAnd edge EkThe sector area is formed; a. thetri(Ek，oi) Is a triangle oip0p1The area of (a).
Further, in A (E)k，Ci) During calculation, if p0Or p1Is located at CiOuter portion of (1), edge EkIn the circle CiThe inner part will be used to calculate the equation A (E)k,Ci) (ii) a If E iskIn the circle CiIf the inner part is not present, A (E)k，Ci) Equal to 0.
A (E) as describedk，Ci) Adding to A (E, C)i) The rule of (1) is as follows:
(a)Cicenter o of circleiInside the characteristic line: if the center of the circle is oiAt the edge EkNormal rear, then A (E)k，Ci) Is a positive number; if the center of the circle is oiAt the edge EkForward of the normal, then A (E)k，Ci) Is a negative number:
wherein EkIs directed to the outside of the characteristic line, neIs the number of characteristic line edges, nkIs edge EkIn the external normal direction, SGN is a function for taking the positive sign;
(b)Cicenter o of circleiOutside the characteristic line, the circle C is calculated according to the above formulaiArea inside the feature line, and sign bit negative:
A(E，Ci)＝Aout(E，Ci)＝πr2+Ain(E，Ci)
the method for approximating each characteristic line generated in the step (2) by a plurality of circles in the step (3) comprises the following steps:
(3-1) initializing, namely dispersing the area surrounded by the characteristic line into boundary points and internal points as points used by L loyd clustering algorithm, and selecting n uniformly distributed on the longest diagonal line of the characteristic linecThe point is taken as the initial position approaching the center of the circle;
(3-2) division: for a point piIn turn, try to divide it into approximate circles Ck(ii) a At this time CkThe radius needs to be increased so that piIs located at CkInner part of, circle CkThe COA of (a) will also increase accordingly; p is a radical ofiWill be divided into circles of minimum COA increments; in which the division order of the dots is to calculate piThe distance to each circle, the minimum value is taken as the priority value of p, and the points with smaller priority values are divided more preferentially;
(3-3) adapting: according to division into approximate circles CkPoint set of (3), adjusting CkCenter o of circleiAnd radius riSo that C iskThe approximation error COA of (c) is minimal, i.e.,
(3-4) deletion and cleavage: if the approximation error Err is not improved significantly in the steps (3-1) and (3-2) which are repeated for a plurality of times, the clustering algorithm falls into local optimum or complete optimum, and at the moment:
(1) dividing the approximate circle with the largest COA into two parts, and dividing the two parts into CiRandomly selecting two points from the points as the centers of two circles;
(2) deleting the circle with the largest coincidence proportion, wherein the coincidence proportion is defined as that the area of the approximation circle overlapped with at least one other circle is divided by the area of the approximation circle;
(3-5) repeating the steps (3-2), (3-3) and (3-4) until one of the following conditions is satisfied:
(1) the approximation error meets the requirement;
(2) iteration reaches a certain number of times;
(3) successive local optima fail to significantly improve the approximation error Err;
at this time, the L loyd clustering algorithm is considered to reach the global optimum, and the best local optimum is taken as the final result.
The significant improvement in the step (3-4) means that the approximation error is reduced to a larger extent, and the standard of the significant improvement is determined according to practical experience.
The method for generating the sphere in the step (4) is that an approximate circle generates a sphere, the center of the sphere is coincident with the center of the circle, and the radius of the sphere is equal to that of the circle; the method for generating the capsule by pairwise matching of the balls on the adjacent characteristic lines is to interpolate the two balls and the interpolation of the balls along the connecting line of the centers of the balls to obtain a geometric body.
The method for automatically adjusting the sizes of the ball and the capsule in the step (5) comprises the following steps:
(5-1) traversing the vertex p of the input three-dimensional human body model, judging whether the vertex p is positioned outside the approximation body, if so, calculating the distances from the vertex p to all balls and all capsules of the approximation body, and if the minimum distance is D, executing 5-2, otherwise, executing 5-3;
(5-2) edge
The radius of the ball is increased by D/2 when the direction is moved by the distance of D/2 of the center of the ball,
refers to the vector from the center o to the vertex p;
(5-3) edge
The direction is moved by a distance of D/2 of the two spherical centers of the capsule, the radius of the two spheres of the capsule is simultaneously increased by D/2,
refers to the vertex p and two spherical centers o1o2From vertical point to vertex point pAnd (5) vector quantity.
In the step (5-1), the distance from the vertex p to all the balls of the approximation body is equal to the distance from the vertex p to the center of the sphere minus the radius of the ball; the distance calculation method from the vertex p to all the capsules of the approximation body in the step (5-1) is as follows: from p to o1o2Making a vertical line to intersect at the point s and intersect with the capsule at the point q, so that the distance from p to the capsule is equal to the distance from p to q; wherein o is1、o2The centers of the two balls of the capsule respectively; if q does not exist, setting the distance to be infinite; the capsule does not include two terminal hemispheres.
The invention can improve the precision by increasing the characteristic lines and increasing the number of circles approaching each characteristic line.
Different from the existing model approximation method, the invention provides a capsule-based human model approximation method, which can quickly obtain a closer and symmetrical human model approximation body and is embodied in the following steps:
(1) converting a three-dimensional approximation problem into a two-dimensional approximation problem by extracting a characteristic line from the three-dimensional human body model;
(2) using L loyd clustering, the user can specify an error threshold by approximating the feature line with a number of circles, the error used being the area of the region inside the circle but not inside the feature line.
Drawings
FIG. 1 is a flow chart of a capsule-based mannequin approximation method provided by the present invention.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, a capsule-based mannequin approximation method includes the steps of:
(1) inputting a three-dimensional human body model;
(2) extracting the characteristic line of the three-dimensional human body model input in the step (1);
(3) approximating each of the characteristic lines generated in step (2) with a plurality of circles;
(4) generating balls according to the circles generated in the step (3); pairing the balls on the adjacent characteristic lines in pairs to generate capsules, and deleting the capsules completely positioned in other capsules;
(5) the sizes of the ball and the capsule are automatically adjusted, so that the human body model is completely positioned in the approaching body.
The three-dimensional human body model in the step (1) can be represented by a triangular mesh or a quadrilateral mesh.
In the step (2), the characteristic line is a boundary line of a cross section of the body part near the joint point and is represented by a polygon.
The characteristic lines include waist, shoulder, neck, elbow, wrist, knee and ankle characteristic lines.
The extraction of the characteristic line can be performed by a manual method or an automatic method.
In the step (3), the approximation method using each characteristic line generated in the step (2) is an iterative L loyd clustering algorithm.
Wherein the number of circles is specified by the user.
The approximation error of the iterative L loyd clustering algorithm is the sum of the areas of the circles in the outer regions of the characteristic line, and is defined as follows:
wherein n iscRepresenting the number of circles used to approximate the characteristic line, E being the set of edges of the characteristic line, A (E, C)i) Represents the ith circle CiThe area outside the characteristic line is denoted as COA.
The area COA of the circle in the outer area of the characteristic line is calculated by adopting a side-by-side calculation method, and the k-th side EkLet p be0、p1Is EkAnd both located at CiInside, the area A (E) corresponding to the sidek，Ci) The calculation is as follows:
A(Ek，Ci)＝Asec(Ek，Ci)-Atri(Ek，oi)
wherein A issec(Ek，Ci) Is a circle CiCenter o of circleiAnd edge EkThe sector area is formed; a. thetri(Ek，oi) Is a triangle oip0p1The area of (a).
At A (E)k，Ci) During calculation, if p0Or p1Is located at CiOuter portion of (1), edge EkIn the circle CiThe inner part will be used to calculate the equation A (E)k,Ci) (ii) a If E iskIn the circle CiIf the inner part is not present, A (E)k，Ci) Equal to 0.
A (E) as describedk，Ci) Adding to A (E, C)i) The rule of (1) is as follows:
(a)Cicenter o of circleiInside the characteristic line: if the center of the circle is oiAt the edge EkNormal rear, then A (E)k，Ci) Is a positive number; if the center of the circle is oiAt the edge EkForward of the normal, then A (E)k，Ci) Is a negative number:
wherein EkIs directed to the outside of the characteristic line, neIs the number of characteristic line edges, nkIs edge EkIn the external normal direction, SGN is a function for taking the positive sign;
(b)Cicenter o of circleiOutside the characteristic line, the circle C is calculated according to the above formulaiArea inside the feature line, and sign bit negative:
A(E，Ci)＝Aout(E，Ci)＝πr2+Ain(E，Ci)
the method for approximating each characteristic line generated in the step (2) by a plurality of circles in the step (3) comprises the following steps:
(3-1) initializing that the area surrounded by the characteristic line is dispersed into boundary points and interior points as LPoints used by the loyd clustering algorithm; selecting n evenly distributed on the longest diagonal of the characteristic linecThe point is taken as the initial position approaching the center of the circle;
(3-2) division: for a point piIn turn, try to divide it into approximate circles Ck(ii) a At this time CkThe radius needs to be increased so that piIs located at CkInner part of, circle CkThe COA of (a) will also increase accordingly; p is a radical ofiWill be divided into circles of minimum COA increments; in which the division order of the dots is to calculate piThe distance to each circle, the minimum value is taken as the priority value of p, and the points with smaller priority values are divided more preferentially;
(3-3) adapting: according to division into approximate circles CkPoint set of (3), adjusting CkCenter o of circleiAnd radius riSo that C iskThe approximation error COA of (c) is minimal, i.e.,
(3-4) deletion and cleavage: if the approximation error Err is not improved significantly in the steps (3-1) and (3-2) which are repeated for a plurality of times, the clustering algorithm falls into local optimum or complete optimum, and at the moment:
(1) dividing the approximate circle with the largest COA into two parts, and dividing the two parts into CiRandomly selecting two points from the points as the centers of two circles;
(2) deleting the circle with the largest coincidence proportion, wherein the coincidence proportion is defined as that the area of the approximation circle overlapped with at least one other circle is divided by the area of the approximation circle;
(3-5) repeating the steps (3-2), (3-3) and (3-4) until one of the following conditions is satisfied:
(1) the approximation error meets the requirement;
(2) iteration reaches a certain number of times;
(3) successive local optima fail to significantly improve the approximation error Err;
at this time, the L loyd clustering algorithm is considered to reach the global optimum, and the best local optimum is taken as the final result.
The significant improvement in the step (3-4) means that the approximation error is reduced to a larger extent, and the standard of the significant improvement is determined according to practical experience.
The method for generating the sphere in the step (4) is that an approximate circle generates a sphere, the center of the sphere is coincident with the center of the circle, and the radius of the sphere is equal to that of the circle; the method for generating the capsule by pairwise matching of the balls on the adjacent characteristic lines is to interpolate the two balls and the interpolation of the balls along the connecting line of the centers of the balls to obtain a geometric body.
The method for automatically adjusting the sizes of the ball and the capsule in the step (5) comprises the following steps:
(5-1) traversing the vertex p of the input three-dimensional human body model, judging whether the vertex p is positioned outside the approximation body, if so, calculating the distances from the vertex p to all balls and all capsules of the approximation body, and if the minimum distance is D, executing 5-2, otherwise, executing 5-3;
(5-2) edge
The radius of the ball is increased by D/2 when the direction is moved by the distance of D/2 of the center of the ball,
refers to the vector from the center o to the vertex p;
(5-3) edge
The direction is moved by a distance of D/2 of the two spherical centers of the capsule, the radius of the two spheres of the capsule is simultaneously increased by D/2,
refers to the vertex p and two spherical centers o1o2Perpendicular to vertex p.
In the step (5-1), the distance from the vertex p to all the balls of the approximation body is equal to the distance from the vertex p to the center of the sphere minus the radius of the ball; the distance calculation method from the vertex p to all the capsules of the approximation body in the step (5-1) is as follows: from p to o1o2The perpendicular line is crossed at the point s and the capsule is crossed at the point q, the distance from p to the capsule is equal to the distance from p to the capsuleThe distance of q; wherein o is1、o2The centers of the two balls of the capsule respectively; if q does not exist, setting the distance to be infinite; the capsule does not include two terminal hemispheres.
The present invention is described in detail with reference to the embodiments, but the embodiments of the present invention are not limited by the embodiments, and any other changes, substitutions, combinations and simplifications made under the teaching of the patent core of the present invention are included in the protection scope of the present invention.
Claims (7)
1. A capsule-based mannequin approximation method comprising the steps of:
(1) inputting a three-dimensional human body model;
(2) extracting the characteristic line of the three-dimensional human body model input in the step (1); the characteristic line is the boundary line of the cross section of the body part near the joint point and is represented by a polygon;
(3) approximating each characteristic line generated in the step (2) by a plurality of circles, wherein the approximation method of each characteristic line generated in the step (2) by a plurality of circles is an iterative L loyd clustering algorithm;
(4) generating balls according to the circles generated in the step (3); pairing the balls on the adjacent characteristic lines in pairs to generate capsules, and deleting the capsules completely positioned in other capsules; the method for generating the sphere comprises the steps of generating a sphere by an approximate circle, wherein the center of the sphere is superposed with the center of the circle, and the radius of the sphere is equal to that of the circle; the method for generating the capsule by pairwise matching the balls on the adjacent characteristic lines is to interpolate the two balls and the interpolation of the balls along the connecting line of the centers of the balls to obtain a geometric body;
(5) the sizes of the ball and the capsule are automatically adjusted, so that the human body model is completely positioned in the approaching body.
2. The capsule-based mannequin approximation method of claim 1, wherein the approximation error of the iterative L loyd clustering algorithm is the sum of areas of circles outside the characteristic line, defined as follows:
wherein n iscRepresenting the number of circles used to approximate the characteristic line, E being the set of edges of the characteristic line, A (E, C)i) Represents the ith circle CiThe area outside the characteristic line is denoted as COA.
3. The capsule-based mannequin approximation method of claim 2, wherein the area COA of the circle in the region outside the characteristic line is calculated by a side-by-side calculation method for the k-th side EkLet p be0、p1Is EkAnd both located at CiInside, the area A (E) corresponding to the sidek，Ci) The calculation is as follows:
A(Ek，Ci)＝Asec(Ek，Ci)-Atri(Ek，oi)
wherein A issec(Ek，Ci) Is a circle CiCenter o of circleiAnd edge EkThe sector area is formed; a. thetri(Ek，oi) Is a triangle oip0p1The area of (a).
4. The capsule-based mannequin approximation method of claim 3, wherein A (E)k，Ci) Adding to A (E, C)i) The rule of (1) is as follows:
(a)Cicenter o of circleiInside the characteristic line, A (E, C) at this timei) Is also denoted as Ain(E，Ci): if the center of the circle is oiAt the edge EkNormal rear, then A (E)k，Ci) Is a positive number; if the center of the circle is oiAt the edge EkForward of the normal, then A (E)k，Ci) Is a negative number:
wherein EkIs directed to the outside of the characteristic line, neIs the number of characteristic line edges, nkIs edge EkIn the external direction of (1), SGN is a function of taking the sign p0 kIs edge EkThe 1 st vertex of (a);
(b)Cicenter o of circleiOutside the characteristic line, A (E, C) at this timei) Is also denoted as Aout(E，Ci) Then, the circle C is calculated according to the above formulaiArea inside the characteristic line, and the sign is negative:
A(E，Ci)＝Aout(E，Ci)＝πr2+Ain(E，Ci)
wherein r is a circle CiOf (c) is used.
5. The capsule-based mannequin approximation method of claim 3, wherein the method of approximating each feature line generated in step (2) with a plurality of circles in step (3) comprises the steps of:
(3-1) initializing, namely dispersing the area surrounded by the characteristic line into boundary points and internal points as points used by L loyd clustering algorithm, and selecting n uniformly distributed on the longest diagonal line of the characteristic linecThe point is taken as the initial position approaching the center of the circle;
(3-2) division: for a point piIn turn, try to divide it into approximate circles Ck(ii) a At this time CkThe radius needs to be increased so that piIs located at CkInner part of, circle CkThe COA of (a) will also increase accordingly; p is a radical ofiWill be divided into circles of minimum COA increments; in which the division order of the dots is to calculate piThe distance to each circle, the minimum value is taken as the priority value of p, and the points with smaller priority values are divided more preferentially;
(3-3) adapting: according to division into approximate circles CkPoint set of (3), adjusting CkCenter o of circleiAnd radius riSo that C iskThe approximation error COA of (c) is minimal, i.e.,
(3-4) deletion and cleavage: if the approximation error Err is not improved significantly in the steps (3-1) and (3-2) which are repeated for a plurality of times, the clustering algorithm falls into local optimum or complete optimum, and at the moment:
(1) dividing the approximate circle with the largest COA into two parts, and dividing the two parts into CiRandomly selecting two points from the points as the centers of two circles;
(2) deleting the circle with the largest coincidence proportion, wherein the coincidence proportion is defined as that the area of the approximation circle overlapped with at least one other circle is divided by the area of the approximation circle;
(3-5) repeating the steps (3-2), (3-3) and (3-4) until one of the following conditions is satisfied:
(1) the approximation error meets the requirement;
(2) iteration reaches a certain number of times;
(3) successive local optima fail to significantly improve the approximation error Err;
at this time, the L loyd clustering algorithm is considered to reach the global optimum, and the best local optimum is taken as the final result.
6. The capsule-based mannequin approximation method of claim 1, wherein the method of automatically adjusting the size of the ball and the capsule in step (5) comprises the steps of:
(5-1) traversing the vertex p of the input three-dimensional human body model, judging whether the vertex p is positioned outside the approximation body, if so, calculating the distances from the vertex p to all balls and all capsules of the approximation body, and if the minimum distance is D, executing 5-2, otherwise, executing 5-3;
(5-2) edge
The direction is moved by a distance of D/2 of the center of the sphere, and the radius of the sphere is increased by D/2,
is the vector from the center o to the vertex p；
(5-3) edge
The direction moves by a distance of D/2 of two spherical centers of the capsule, and the radius of the two spheres of the capsule is simultaneously increased by D/2,
refers to a vector from vertex s to vertex p, s being p to line segment o1o2Is used for the foot drop.
7. The capsule-based mannequin approximation method of claim 6, wherein the distance from the apex p to all balls of the approximation body in step (5-1) is equal to the distance from p to the center of the ball minus the radius of the ball; the distance calculation method from the vertex p to all the capsules of the approximation body in the step (5-1) is as follows: from p to o1o2Making a vertical line to intersect at the point s and intersect with the capsule at the point q, so that the distance from p to the capsule is equal to the distance from p to q; wherein o is1、o2The centers of the two balls of the capsule respectively; if s is located on the line segment o1o2The distance is set to infinity.
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