CN107992672A - A kind of soft tissue deformation modeling method based on virtual spring - Google Patents
A kind of soft tissue deformation modeling method based on virtual spring Download PDFInfo
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Abstract
The invention discloses a kind of soft tissue deformation modeling method of the soft tissue shape present invention based on virtual spring based on virtual spring, based on mass-spring modeling, establish a kind of real-time deformation model of improved soft tissue, by square with the topological structure soft tissue surfaces model that isosceles right triangle is combined, virtual volumetric spring is added, realizes more real deformation effects；In systems at each particle, the superposition of surface spring deformation amount is equivalent to body surface deformation, the contact force for making a concerted effort to be equivalent to body surface of virtual spring elastic force；The principle of the classical mass-spring modeling of this model inheritance is simple, easily modeling, the advantages that calculating speed is fast, while also have the ability of control deformed region.
Description
Technical field
The invention belongs to virtual reality human-computer interaction technical field, more specifically, is related to one kind and is based on virtual spring
Soft tissue deformation modeling method.
Background technology
A key technology during human body soft tissue deformation techniques virtual emulation, in virtual environment power haptic interaction
During, establish the power haptic model based on physical significance and be very important.The physical deformation mould of current most of soft tissues
Type is all based on elastic theory research.Majumder etc. proposes the soft tissue with physical significance based on finite element method (FEM)
Deformation model, although accurately, requiring the number of nodes of grid, calculating of high cost.Peterlik etc. proposes nonlinear finite element mould
Type, improves and constantly thinks, but still it is impossible to meet the frequency requirement of haptic device thousand hertz.Wang etc. uses boundary element
Method establishes model, although having been carried out to the border of model discrete, simplifies calculating, exists in terms of stability certain
It is difficult.The it is proposeds such as Zhong have the Reaction-diffusion terms surface model of physicochemical characteristics, it is difficult to carry out the operation of complex precise.
Chen proposed the triangular surface mesh topology model based on spring-mass in 2006, and modular concept is simple, but
It is that stability has much room for improvement.The present Research that Xu lacks Soft tissue cutting model of the equality based on mesh free is analyzed, and is referred to
Go out its following developing direction, but stability is poor.Wu Juan etc. proposes one kind and is based on radially being divided into concentric circles
The spring-mass model and real-time force of distribution feel response algorithm, but model each point calculating is inconsistent, is not easy to extend.Bullet
Spring-Mass Model principle is simple, easily modeling, disclosure satisfy that real-time interactive operation requirement, but precision has much room for improvement.Therefore, exist
While ensureing distorted pattern accuracy, the real-time of calculating is improved, is that current virtual power haptic-display system is urgently to be resolved hurrily
Problem.
From the perspective of biomethanics, skin, the soft tissue of fats portion can be approximately considered is isotropism and homogeneous
's.But since soft tissue is under stress, all in real-time change, this to be based on kinematics the size and Orientation of stress surface
Solution to model will necessarily produce concussion.Traditional model based on surface network topological structure, in simulation soft tissue deformation process
Middle stability is poor, it is impossible to shows the biomechanics characteristic of soft tissue well.
The content of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of soft tissue deformation based on virtual spring
Modeling method, truly reflects the physical deformation process of soft tissue by establishing spring-mass model.
For achieving the above object, a kind of soft tissue deformation modeling method based on virtual spring of the present invention, its feature
It is, comprises the following steps：
(1), soft tissue geometrical model is obtained
By image data, the geometrical model of tissue is established and rendered based on OpenGL, and is shown by display
Geometrical model；
(2), the soft tissue physical model with virtual spring is established according to geometrical model
The contact point n of virtual spring and changing object is determined first0, with contact point n0Centered on radiated around,
Whole changing object is divided into m layers of concentric loops, wherein, contact layer from contact point to four direction homogeneous radiation so that
Building has the function of the soft tissue physical model of virtual spring；
(3), feedback force is calculated according to deformation quantity
(3.1), according to dynamic balance relation, the stressing conditions at contact point is analyzed, are had：
Wherein,Represent contact point n0The normal force at place,Represent first layer particle tangential force,Represent contact point n0
Locate the coefficient of elasticity of virtual spring, θ1For particle n after deformation1With contact point n0The horizontal direction angle of line, Δ Z0Expression connects
The deformation length of displacement at contact, i.e. virtual spring, Δ r1Represent the deformation quantity of tangential adjacent particle surface spring, i.e.,
So, the stressing conditions of i-th layer of particle have the deformation quantity of contact point and first layer particle surface spring：
Wherein, i=1,2 ..., m,Represent i-th layer of particle tangential force,Represent i-th layer of particle normal force,Represent
Particle n in i-th layeriThe virtual spring coefficient of elasticity at place, Δ ZiRepresent particle n in i-th layeriThe displacement at place, i.e. virtual spring
Deformation length, θiFor particle n after deformationiWith particle ni-1Line and horizontal direction angle；
(3.2), each layer virtual spring deformation quantity is analyzed
As i=m, obtained by formula (1) and formula (2)
I.e.
According to the force analysis of model normal plane, the normal deformation amount Δ Z of each layer particle has following relationship
Wherein, liFor the deformation quantity of i-th layer of particle normal direction virtual spring；
If the coefficient of elasticity of tangential surface spring in each layerIt is equal, then is released by formula (1)：
Wherein, r be surface spring original length, Δ riRepresent the deformation quantity of tangential adjacent particle surface spring；
OrderFor the deformation ratio of the tangential surface spring of i-th layer of spring, it is brought into (8) formula, and make αi=2i+
1, it can obtain as follows on surface spring deformation rate and αiBetween relational expression：
Wherein, ε1The deformation ratio of the tangential surface spring of first layer is then represented, normal direction can be derived according to geometrical relationship
The deformation quantity l of upper i-th layer of particle normal direction virtual springiFor：
As i=1, haveCan further it derive
Surface spring deformation rate, 1st layer particle normal direction of the deformation quantity of i.e. i-th layer particle normal direction virtual spring by the 1st layer
The deformation quantity and number of plies i of virtual spring determine；
(3.3), analyze feedback force and propagate the relation between the number of plies：
If the propagation number of plies is m, i.e., as i=m, then have：
Wherein,Represent the deformation quantity on zoning border, and boundary parameter；
After have selected the m in calculating, sin θ can be approx thoughtm+1≈ 0, at this time, formula (4) are changed into：
(4), according to the symmetry of model, the deformation quantity size of each particle in model and anti-is calculated according to the method described above
The size of power is presented, so as to establish spring-mass model；
(5), the spring-mass model established is imported into interactive device by computer software and carries out auxiliary realization,
When colliding, model deformation module updates the position of contact point according to paracentesis depth, obtains Δ Z, according to propagation depth m
Deformation region is calculated, model rendering figure is updated in virtual scene, so as to set up soft tissue deformation model；Meanwhile according to
Δ Z calculates the size of feedback force F, allow operator can real-time experience to effect force feedback.
What the goal of the invention of the present invention was realized in：
Meanwhile soft tissue deformation modeling of the soft tissue shape present invention of the invention based on virtual spring based on virtual spring
Method, based on spring-mass model, establishes a kind of real-time deformation model of improved soft tissue, by straight with isosceles in square
In the topological structure soft tissue surfaces model that angle triangle is combined, virtual volumetric spring is added, realizes more real deformation
Effect；In systems at each particle, the superposition of surface spring deformation amount is equivalent to body surface deformation, virtual spring elasticity
The contact force for making a concerted effort to be equivalent to body surface of power；The principle of the classical mass-spring modeling of this model inheritance is simple, Yi Jian
The advantages that mould, fast calculating speed, while also there is the ability of control deformed region.
Become modeling method also to have the advantages that：
(1), the foundation of model employs the structure that isosceles right triangle is combined with square, and it is preferable right to have
Title property and repeatability, deformation region regular shape, so that calculation amount is small, ensure that high when force feedback calculates refresh
The requirement of frequency, so as to reach, simulation effect is true to nature, and the relative displacement of each particle and the superposition of elastic force are equivalent to soft tissue
Deformation and contact force；
(2), the present invention is provided with virtual volumetric spring during modeling so that has in surface model deformation process
The information of body；
(3), good effect can be obtained by carrying out pressing deformation simulation by the instrument on haptic interaction device, can
Meet the requirement of the authenticity of interactive system, stability and real-time；
(4), present invention could apply to virtual surgery emulation, tele-medicine, guide to help the disabled, virtual game amusement
The multiple fields such as industry.
Brief description of the drawings
Fig. 1 is the soft tissue deformation modeling method flow chart of the invention based on virtual spring；
Fig. 2 is provided with the soft tissue physical model of virtual spring；
Fig. 3 deformation normal plane a direction section.
Embodiment
The embodiment of the present invention is described below in conjunction with the accompanying drawings, so that those skilled in the art is more preferable
Ground understands the present invention.Requiring particular attention is that in the following description, when known function and the detailed description of design
When perhaps can desalinate the main contents of the present invention, these descriptions will be ignored herein.
Embodiment
Fig. 1 is the soft tissue deformation modeling method flow chart of the invention based on virtual spring.
A kind of complete virtual flexible body haptic device emulation decorum includes main frame and power haptic interaction is set
It is standby, display is connected with main frame, computer is linked with power haptic interaction device, for that will calculate deformation module
The soft tissue surfaces deformation data of generation is transmitted to power haptic interaction device.The haptic interaction device used in example is
The PHANTOM equipment of SensAble scientific ＆ technical corporation, can accurately track the three-dimensional motion of human hand, and will be calculated by dummy model
Fictitious force feed back to operator in real time, power feel on feeling of immersion true to nature is provided.The maximum output of PHANTOM equipment is anti-
Feedback power is 3.3N.
This example is by medical image data, the geometrical model of soft tissue, Ran Hou are established and rendered based on OpenGL
The spring-mass model designed by using the method for the present invention is added in the geometrical model of three-dimensionalreconstruction, enables soft tissue true
Reflect the physical deformation process of organ on the spot.Then in virtual scene, virtual operation instrument model and soft tissue mould are established
Type, imports in the Simulink of Matlab and establishes simulation model.In collision detection module, the interaction of virtual operation instrument is determined
Position is controlled with force feedback equipment by tactile nib.When colliding, program calculates feedback force according to paracentesis depth Δ Z
Size, operator can real-time experience to effect force feedback.Meanwhile model deformation module is according to paracentesis depth real-time update
The position of contact point, calculates deformation region according to depth m is propagated, model rendering figure is updated in virtual scene, there is provided vision
Feedback.
In the present embodiment, as shown in Figure 1, a kind of soft tissue deformation modeling method based on virtual spring of the present invention, bag
Include following steps：
S1, obtain soft tissue geometrical model
By image data, the geometrical model of tissue is established and rendered based on OpenGL, and is shown by display
Geometrical model；
S2, establish the soft tissue physical model with virtual spring according to geometrical model
To establish virtual soft tissue Real-time force feedback interactive system, established according to geometrical model has virtual spring first
The soft tissue physical model of function, in example using the isosceles right triangle proposed by the present invention equipped with virtual volumetric spring and
The structural model that square is combined, each particle in a model devise a virtual volumetric spring, virtual volumetric spring with
Impact direction is consistent, and is dynamically produced when emulation proceeds by；
The contact point n of virtual spring and changing object is determined first0, with contact point n0Centered on radiated around,
Whole changing object is divided into m layers of concentric loops, as shown in Fig. 2, wherein, contact layer is equal from contact point to four direction
Even radiation, first layer have 4 particles, 4 springs, and the second layer has 8 particles, 12 springs, and third layer has 12 particles, and 20
A spring, and so on, 4 particles of every layer of increase, 8 springs, then m layers have 4m particle, 4 (2m-1) a springs；Its
In, each layer of shape is all square, and the particle rigid connection in same layer, adjacent interlayer the elastic coefficient is identical, from
And build the soft tissue physical model with virtual spring；
S3, according to deformation quantity calculate feedback force
S3.1, the model to above-mentioned foundation carry out the calculating of analysis and the force feedback of power, when F acts on particle n0When,
n0Leave initial position under force to deform upon, at this time n0The virtual volumetric spring at place is had an effect.Move down at the same time
Particle n0Adjacent layer particle is driven to be subjected to displacement by surface spring, virtual volumetric spring is also sent out at each particle being subjected to displacement
Raw effect.Locate particle n when equilibrium is reached0Move to n '0.A direction of stress normal plane is taken to be analyzed in example, such as
Shown in Fig. 3, the displacement of particle is exactly the deformation length of virtual spring.According to spring deformation length, the deformations between adjacent layer
Relation between the interface of position and particle deformation position extrapolates the normal deformation amount of each layer particle, and then calculates whole mould
The size of type deformation region and the size of feedback force.The stressing conditions at contact point are analyzed, are had according to dynamic balance relation：
Wherein,Represent contact point n0The normal force at place,Represent first layer particle tangential force,Represent contact point n0
Locate the coefficient of elasticity of virtual spring, θ1For particle n after deformation1With contact point n0The horizontal direction angle of line, Δ Z0Expression connects
The deformation length of displacement at contact, i.e. virtual spring, Δ r1Represent the deformation quantity of tangential adjacent particle surface spring, i.e.,
So, the stressing conditions of i-th layer of particle have the deformation quantity of contact point and first layer particle surface spring：
Wherein, i=1,2 ..., m, fTiRepresent i-th layer of particle tangential force,Represent i-th layer of particle normal force,Represent
Particle n in i-th layeriThe virtual spring coefficient of elasticity at place, Δ ZiRepresent particle n in i-th layeriThe displacement at place, i.e. virtual spring
Deformation length, θiFor particle n after deformationiWith particle ni-1Line and horizontal direction angle；
S3.2, each layer virtual spring deformation quantity of analysis
As i=m, obtained by formula (1) and formula (2)
I.e.
According to the force analysis of model normal plane, under paracentesis depth, that is, normal deformation amount Δ Z of each layer particle has
Row relation：
Wherein, liFor the deformation quantity of i-th layer of particle normal direction virtual spring；
If the coefficient of elasticity of tangential surface spring in each layerIt is equal, then is released by formula (1)：
Wherein, r be surface spring original length, Δ riRepresent the deformation quantity of tangential adjacent particle surface spring；
OrderFor the deformation ratio of the tangential surface spring of i-th layer of spring, it is brought into (8) formula, and make αi=2i+
1, it can obtain as follows on surface spring deformation rate and αiBetween relational expression：
Wherein, ε1The deformation ratio of the tangential surface spring of first layer is then represented, normal direction can be derived according to geometrical relationship
The deformation quantity l of upper i-th layer of particle normal direction virtual springiFor：
As i=1, haveCan further it derive
Surface spring deformation rate, 1st layer particle normal direction of the deformation quantity of i.e. i-th layer particle normal direction virtual spring by the 1st layer
The deformation quantity and number of plies i of virtual spring determine；
Relation between S3.3, analysis feedback force and the propagation number of plies：
In a model, the size of calculation amount is substantially dependent on propagating the size of depth, that is, propagates number of stories m
Size, if the propagation number of plies is m, i.e., as i=m, then has：
Wherein,Represent the deformation quantity on zoning border, and boundary parameter；
After have selected the m in calculating, sin θ can be approx thoughtm+1≈ 0, at this time, formula (4) are changed into：
S4, the symmetry according to model, calculate the deformation quantity size and feedback of each particle in model according to the method described above
The size of power, so as to establish spring-mass model；
S5, imported into interactive device by computer software by the spring-mass model established and carry out auxiliary realization,
When colliding, model deformation module updates the position of contact point according to paracentesis depth, obtains Δ Z, according to propagation depth m
Deformation region is calculated, model rendering figure is updated in virtual scene, so as to set up soft tissue deformation model；Meanwhile according to
Δ Z calculates the size of feedback force F, allow operator can real-time experience to effect force feedback.
Example
The deformation simulation of soft tissue Real-time force feedback interactive system generally requires higher real-time, therefore to system
Calculating speed and refreshing frequency have very high requirement.It is required that vision, power, which feel to reproduce, has continuity, soft group of visual display
Knit deformation refreshing frequency and be not less than 30Hz, power feels that the refreshing frequency reproduced should be wanted in more than 1kHz to reach force feedback
That asks has the characteristics that rapidity.
As contact point deformation ratio ε1When taking different value, different inflection curves are obtained.Also, under the action of identical power,
The deformation ratio ε of different tissues1Difference, the deformation of soft tissue are also different.ε1It is bigger, show that soft tissue is more soft, stress deformation is got over
Greatly.Meanwhile the pliability of soft tissue also with virtual volumetric spring coefficient of elasticity KNSize it is related, choosing KNWhen should examine
The size of model deformation is considered, it is also contemplated that the restraining factors of the force feedback equipment feedback force upper limit, power output F is made according to formula (14)
Less than equipment maximum output value, in this example, less than 3.3N.
It is a parameter for controlling deformation region to propagate depth m, its size not only affects the size of calculation amount, and
And affect computational accuracy.When the timing of deformation paracentesis depth one, propagation depth m is bigger, and accuracy is higher, and feedback force is closer
True power.The problem of in view of calculation amount, determine according to actual conditions in example to propagate the size of depth m, according to formula (13),
Take virtual spring coefficient of elasticity KN0=50N/m, r=0.002m are tested, and obtain feedback force with propagating the corresponding pass of depth m
System.
By formula (12) it is recognised that the size of m is by lm/ r and ε1Together decide on, choose m=25.Surface spring original length
R is regular length.According to formula (5) and formula (11), soft tissue virtual spring deformation quantity and propagation depth m during stress can be obtained
Relation.
Although the illustrative embodiment of the present invention is described above, in order to the skill of the art
Art personnel understand the present invention, it should be apparent that the invention is not restricted to the scope of embodiment, to the general of the art
For logical technical staff, if various change appended claim limit and definite the spirit and scope of the present invention in,
These changes are it will be apparent that all utilize the innovation and creation of present inventive concept in the row of protection.
Claims (3)
1. a kind of soft tissue deformation modeling method based on virtual spring, it is characterised in that comprise the following steps：
(1), soft tissue geometrical model is obtained
By image data, the geometrical model of tissue is established and rendered based on OpenGL, and geometry is shown by display
Model；
(2), the soft tissue physical model with virtual spring is established according to geometrical model
The contact point n of virtual spring and changing object is determined first0, with contact point n0Centered on radiated around, will be whole
Changing object is divided into m layers of concentric loops, wherein, contact layer is from contact point to four direction homogeneous radiation, so as to build
There is the soft tissue physical model of virtual spring；
(3), feedback force is calculated according to deformation quantity
(3.1), according to dynamic balance relation, the stressing conditions at contact point is analyzed, are had：
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Intend the coefficient of elasticity of spring, θ1For particle n after deformation1With contact point n0The horizontal direction angle of line, Δ Z0Represent at contact point
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Wherein, i=1,2 ..., m,Represent the particle tangential force,Represent i-th layer of particle normal force,Represent i-th layer
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As i=m, obtained by formula (1) and formula (2)
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<mi>l</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;Z</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>l</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mo>...</mo>
<mo>+</mo>
<msub>
<mi>l</mi>
<mi>m</mi>
</msub>
<mo>+</mo>
<msub>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;Z</mi>
<mi>m</mi>
</msub>
<mo>=</mo>
<msub>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
If the coefficient of elasticity of tangential surface spring in each layerIt is equal, then is released by formula (1)：
<mrow>
<mn>4</mn>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>K</mi>
<msub>
<mi>T</mi>
<mi>i</mi>
</msub>
</msub>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
<mfrac>
<mi>r</mi>
<mrow>
<mi>r</mi>
<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mo>&lsqb;</mo>
<mn>8</mn>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<mo>&rsqb;</mo>
<msub>
<mi>K</mi>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</msub>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mfrac>
<mi>r</mi>
<mrow>
<mi>r</mi>
<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
<mi>r</mi>
<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mi>r</mi>
<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mfrac>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mn>1</mn>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
</mrow>
<mrow>
<mi>r</mi>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mn>1</mn>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, r be surface spring original length, Δ riRepresent the deformation quantity of tangential adjacent particle surface spring；
OrderFor the deformation ratio of the tangential surface spring of i-th layer of spring, it is brought into (8) formula, and make αi=2i+1, can be with
Obtain as follows on surface spring deformation rate and αiBetween relational expression：
<mrow>
<msub>
<mi>&epsiv;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
<mrow>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, ε1The deformation ratio of the tangential surface spring of first layer is then represented, can be derived i-th in normal direction according to geometrical relationship
The deformation quantity l of layer particle normal direction virtual springiFor：
<mrow>
<msub>
<mi>l</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>=</mo>
<mi>r</mi>
<msqrt>
<mrow>
<mo>(</mo>
<mn>2</mn>
<msub>
<mi>&epsiv;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msup>
<msub>
<mi>&epsiv;</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
As i=1, haveCan further it derive
<mrow>
<msub>
<mi>l</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msqrt>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
</msqrt>
</mfrac>
<mfrac>
<mn>1</mn>
<msqrt>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
</msqrt>
</mfrac>
<msub>
<mi>l</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
The deformation quantity of i.e. i-th layer particle normal direction virtual spring by the 1st layer surface spring deformation rate, the 1st layer of particle normal direction it is virtual
The deformation quantity and number of plies i of spring determine；
(3.3), analyze feedback force and propagate the relation between the number of plies：
If the propagation number of plies is m, i.e., as i=m, then have：
<mrow>
<mi>m</mi>
<mo>=</mo>
<mfrac>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>r</mi>
<msub>
<mi>l</mi>
<mi>m</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,Represent the deformation quantity on zoning border, and boundary parameter；
After have selected the m in calculating, sin θ can be approx thoughtm+1≈ 0, at this time, formula (4) are changed into：
<mrow>
<mi>F</mi>
<mo>=</mo>
<msub>
<mi>K</mi>
<msub>
<mi>N</mi>
<mn>0</mn>
</msub>
</msub>
<msub>
<mi>&Delta;Z</mi>
<mn>0</mn>
</msub>
<mo>_</mo>
<msub>
<mi>K</mi>
<msub>
<mi>N</mi>
<mn>0</mn>
</msub>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mn>4</mn>
<mi>i</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>&Delta;Z</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
(4), according to the symmetry of model, the deformation quantity size and feedback force of each particle in model are calculated according to the method described above
Size, so as to establish spring-mass model；
(5), the spring-mass model established is imported into interactive device by computer software and carries out auxiliary realization, work as hair
During raw collision, model deformation module updates the position of contact point according to paracentesis depth, obtains Δ Z, is calculated according to depth m is propagated
Deformation region, updates model rendering figure, so as to set up soft tissue deformation model in virtual scene；Meanwhile calculated according to Δ Z
Go out the size of feedback force F, allow operator can real-time experience to effect force feedback.
2. a kind of soft tissue deformation modeling method based on virtual spring according to claim 1, it is characterised in that described
Soft tissue physical model using isosceles right triangle with the model that is combined of square, each particle in model designs
One virtual volumetric spring, virtual volumetric spring is consistent with Impact direction, and dynamically produced when emulation proceeds by.
A kind of 3. soft tissue deformation modeling method based on virtual spring according to claim 1 or 2, it is characterised in that
The soft tissue physical model has following features：
Each layer of shape is all square, the particle rigid connection in same layer, and adjacent interlayer the elastic coefficient is identical；Its
In, first layer has 4 particles, 4 springs, and the second layer has 8 particles, 12 springs, and third layer has 12 particles, 20 bullets
Spring, and so on, 4 particles of every layer of increase, 8 springs, then m layers have 4m particle, 4 (2m-1) a springs.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108874125A (en) * | 2018-05-28 | 2018-11-23 | 徐州昇科源信息技术有限公司 | A kind of virtual skin surface Real-time force feedback interactive system |
| CN109739360A (en) * | 2019-01-07 | 2019-05-10 | 东北大学 | A kind of control system and method that device for force feedback emulates human body soft tissue |
| CN110046406A (en) * | 2019-03-28 | 2019-07-23 | 天津大学 | A kind of soft tissue emulation mode with force feedback structure in anatomic teaching system |
| CN112233253A (en) * | 2020-12-14 | 2021-01-15 | 成都完美时空网络技术有限公司 | Virtual sphere deformation control method and device, electronic equipment and storage medium |
| CN113343513A (en) * | 2021-05-11 | 2021-09-03 | 南京信息工程大学 | Method and device for simulating soft tissue deformation and path cutting |
| CN113409443A (en) * | 2021-05-19 | 2021-09-17 | 南昌大学 | Soft tissue modeling method based on position constraint and nonlinear spring |
| CN114117835A (en) * | 2021-07-28 | 2022-03-01 | 上海华模科技有限公司 | Eyeball modeling method in ophthalmologic operation simulation trainer |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108874125A (en) * | 2018-05-28 | 2018-11-23 | 徐州昇科源信息技术有限公司 | A kind of virtual skin surface Real-time force feedback interactive system |
| CN109739360A (en) * | 2019-01-07 | 2019-05-10 | 东北大学 | A kind of control system and method that device for force feedback emulates human body soft tissue |
| CN110046406A (en) * | 2019-03-28 | 2019-07-23 | 天津大学 | A kind of soft tissue emulation mode with force feedback structure in anatomic teaching system |
| CN110046406B (en) * | 2019-03-28 | 2022-07-05 | 天津大学 | Soft tissue simulation method with force feedback structure in anatomical teaching system |
| CN112233253A (en) * | 2020-12-14 | 2021-01-15 | 成都完美时空网络技术有限公司 | Virtual sphere deformation control method and device, electronic equipment and storage medium |
| CN112233253B (en) * | 2020-12-14 | 2021-03-16 | 成都完美时空网络技术有限公司 | Virtual sphere deformation control method and device, electronic equipment and storage medium |
| CN113343513A (en) * | 2021-05-11 | 2021-09-03 | 南京信息工程大学 | Method and device for simulating soft tissue deformation and path cutting |
| CN113409443A (en) * | 2021-05-19 | 2021-09-17 | 南昌大学 | Soft tissue modeling method based on position constraint and nonlinear spring |
| CN114117835A (en) * | 2021-07-28 | 2022-03-01 | 上海华模科技有限公司 | Eyeball modeling method in ophthalmologic operation simulation trainer |
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