CN106874563A - A kind of deformable component Fast design method based on space constraint - Google Patents
A kind of deformable component Fast design method based on space constraint Download PDFInfo
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Abstract
The invention discloses a kind of deformable component Fast design method based on space constraint, comprise the following steps：1. the space constraint border of target element is extracted；2. simplified Mass-spring Model is set up, deformable component is initialized in constraint space, the free wxpansion of deformable component is simulated by gradually incremental air pressure, and carry out Mechanical Analysis of Particles；3. the equation of motion of particle is solved, and the numerical integration that the particle spring system equation of motion is carried out using Verlet integration methods is solved；4. collision detection is carried out, the collision problem between deformable component and constraint space border is processed using the collision checking method based on AABB bounding volumetrees；5. whether judgment models reach satisfied shape；6. the volume of target element is calculated, judges whether to reach predetermined volume.The present invention establishes simplified Mass-spring Model structure, using the deformation process of the strict Controlling model of accurate collision checking method, is remarkably improved the design efficiency of deformable product.
Description
Technical field
The invention belongs to the shape-designing technical field in the design of industrial deformable product, and in particular to one kind is based on space
The deformable component Fast design method of constraint.
Background technology
In modernization design, the design of product is generally subject to the requirement of product self performance, assembly environment and processing work
The restriction of the factors such as skill, is the spatial design problem under a multiple constraint effect.Modern product is mostly to collect mechanical, electrical, liquid in one
The complication system of body, its component part is not only large number of, and complex structure.Except standardized component, for example, start mechanical, electrical
Beyond gas element etc., also including the deformable component in part.The class component is on the premise of itself functional requirement is met without fixation
Profile, with larger design freedom, but its design constraint is usual and complex, is a difficulty in product design
Point.By taking automotive oil tank design as an example, to realize the compact layout of vehicle, volume of fuel tank requirement should be ensured in the design, and not
Locus interference can occur with the parts of other on automobile chassis, design is generally needed in order to obtain satisfied design effect
Personnel are changed the threedimensional model for designing repeatedly.However, in existing 3D sculpting software, the establishment of free form surface and
Modification is considerably complicated, and labour intensity is larger, has had a strong impact on the efficiency of product design.
At present, the method on model virtual deformable modeling is broadly divided into two classes：Method based on geometry and based on physics
Method.A kind of important form of the deformable bodies modeling method based on geometry is the deformation method based on grid model.Such as
《Geometric modeling based on polygonal meshes》(Botsch M,Pauly M,Kobbelt L,et
al.Proc of the Acm Siggraph Course Notes,2007,29(29):Mentioned in 432-41.) using grid list
The form of unit's set describes deformable bodies, and it is mainly characterized by being put down by carrying out geometry to features such as grid vertex, borders
The operations such as shifting, rotation and the merging and fractionation of patch grids change the effect of mould shapes to reach.Yet with expression thing
The number of grid of body is numerous, and Direct Modeling is relatively difficult, operation is carried out to a single point or dough sheet and is difficult to make model produce significantly
And significant deformation.Therefore, physically-based deformation method is of increased attention.Mass-spring therein
Model method, the stress of particle is directly to be obtained from force analysis, therefore computational efficiency is higher.In addition, mass spring model
Largely increase and time-consuming non-intuitive deficiency because constructing the control node of complex model when not only overcoming Geometric Modeling, also realize
Real world is emulated, the expression problem of the unknown deformable body object of net shape is solved, therefore in fabric, face
Emulation, surgical field are received and are widely applied, but application in engineering moulding field is then more rare.Such as
《Developing alternative design concepts in VR environments using volumetric
self-organizing feature maps》(Igwe P C,Knopf G K,Canas R.Journal of
Intelligent Manufacturing,2008,19(6):661-675.) the deformable physical model of Mass-spring is used to produce
The conceptual design of product, this is that mass spring model is once attempted well in terms of product design, but they only consider
The stress and deformation of single body, the more difficult control of object deformation is not suitable for the deformation of the deformable component with complex space constraint
Process simulation.
In sum, in the existing deformable component shape-designing method with complex space constraint, not enough main body
Present following two aspects：1., based on existing 3D sculpting software is to the establishment of free form surface and changes considerably complicated, exist
The problem that time-consuming, efficiency is low；2. the Mass-spring Physical Modeling of simplification is utilized in current research for the concept of product
Design has that scope of design is narrow, deformation is more rambunctious.
The content of the invention
It is an object of the invention to be directed to above mentioned problem of the prior art, there is provided a kind of based on the deformable of space constraint
Component Fast design method, flexible article deformation simulative technology is applied to the shape-designing neck of deformable component in complex product
Domain.
For achieving the above object, present invention employs following technical scheme：
A kind of deformable component Fast design method based on space constraint, comprises the following steps：
Step 1：According to the design requirement and assembly environment of product, the space constraint border of target element is extracted；
Step 2：Simplified mass spring model is set up, its particle is all distributed in model surface, and only adjacent
It is attached by spring between two particles；Deformable component is initialized in constraint space, by gradually incremental air pressure come
The free wxpansion of deformable component is simulated, and carries out Mechanical Analysis of Particles；The gravity and frictional force of particle are to realizing deformable group
Part is designed without practical significance, and its value is set as 0, therefore the main stress of particle is spring force, particle movement damping force and inside
Gas pressure；
Step 3：The equation of motion of particle is solved, Mass-spring Equation of Motion is carried out using Verlet integration methods
Numerical integration solve；
Step 4：Collision detection is carried out, deformable component is processed using the collision checking method based on AABB bounding volumetrees
With the collision problem between constraint space border, execution step 5 or step 6 are then gone to；
Step 5：Whether judgment models reach satisfied shape, and deformation simulative is terminated if satisfied, and deformation terminates；If discontented
Meaning then re-executes step 2；
Step 6：The volume of target element is calculated, judges whether to reach predetermined volume, deformed if reaching and terminate；If reaching
Less than then re-executing step 2.
The mass spring model of above-mentioned steps 2, the equation of motion of its system is equation below：
In formula, M is the mass matrix of system, and X is the locus of particle, and t is the time for increasing gas pressure, Fk、FdWith
FpThe respectively gentle body pressure matrix of the spring force matrix of particle system, damping force matrix；
If the spring between particle is preferable Hookean spring, Hooke's law is obeyed, and ignore camber of spring damping, with
Each connected spring of particle effect all strong to the particle, it is assumed that have j by the adjacent particle that spring is connected with particle i
It is individual, according to Hooke's law, act on the spring force on particle i and make a concerted effort to be expressed as formula：
In formula,For the spring force that particle i is subject to is made a concerted effort, E is the adjacent point set between particle i with spring connection,
kijIt is the spring rate between particle i and j, xiWith xjIt is particle i and positions of the j in time t,It is bullet between particle i and j
The original of spring is long；
The damping force being subject in particle movement is directly proportional to the movement velocity of particle, then damping force is expressed as formula：
In formula,For the damping force that particle movement is subject to；C is damped coefficient, and v is the movement velocity of particle i；
Act on the gas pressure on particle i and be equal to the gas that gas is produced on each tri patch adjacent with particle i
Body pressure sum；For perfect gas, according to Clausius-Clapeyron equations, the gas pressure being subject on particle i is represented
It is equation below：
In formula,It is the gas pressure that particle i is subject to, Tri is the tri patch collection for sharing particle i, AikIt is and particle i
The area of connected triangle k,It is the outer normal vector of tri patch；
The equation of motion of the solution particle of above-mentioned steps 3 is that ((t- Δs t) is respectively adopted t+ Δ t) with x by particle position x
Taylor's formula is launched, then obtain equation below：X (t+ Δs t)=2x (t)-x (t- Δ t)+M-1F[x(t),v(t)]Δt2；
In formula, (t+ Δs t) is respectively t and the (rate matrices of t+ Δ t) moment particle systems for v (t) and v；X (t) and x
(t+ Δs t) is respectively t and the (transposed matrix of t+ Δ t) moment particle systems；F [x (t), v (t)] is t particle-bullet
The matrix of making a concerted effort being subject to of spring system.
The algorithm steps of the collision detection of above-mentioned steps 4 are as follows：
Step 4.1：Deformable component is set up using Octree space partitioning method to be surrounded with the level on constraint space border
Tree construction；
Step 4.2：Simulated time step is performed, x (t+ Δ t), and to now deformable group are calculated according to x (t)
The Bounding Box of part is updated；
Step 4.3：To carrying out bounding box test for intersection between deformable component and constraint space border, find and interfere
Bottom bounding box pair；
Step 4.4：Bottom bounding box to interfering carries out collision detection of high precision to internal geometric units, until looking for
Go out all particles and triangular unit for colliding, then update particle position, speed and stress, display model.
In above-mentioned steps 4.4, after specific collision cell is found, to (particle position at t+ Δ t) moment is modified,
The coordinate representation equation below put after correction position：
In formula, Δ t is time step, and d is penetrated into the depth inside constraint space for particle, and (t+ Δs t) is matter for P (t) and P
Point P is in t and the (position of t+ Δs t).
The volume of the target element of above-mentioned steps 6 be calculated as by deformable component to triangle gridding dough sheet and coordinate
The discrete tetrahedron volume constituted between origin is integrated, so that the volume of target element is expressed as formula：
In formula, Vi1x、Vi1yAnd Vi1zThe three dimensional space coordinate of the particle i1 respectively on tri patch, Vi2x、Vi2yAnd Vi2z
The three dimensional space coordinate of the particle i2 respectively on tri patch, Vi3x、Vi3yAnd Vi3zParticle i3's respectively on tri patch
Three dimensional space coordinate, and arranged in counter clockwise direction around its exterior normal in these three particles.
Compared to prior art, advantage of the invention is that：
It is of the invention to propose a kind of deformable component Fast design method based on space constraint, by the modeling of deformable component
Into the flexible article with certain space volume, by giving suitable stress, deformation and constraints, make it virtual
Dilatancy and design requirement is finally reached in assembly environment；Using the deformation of the strict Controlling model of accurate collision checking method
Process, can prevent deformable component from being interfered with other assemblies, so that ensure the assembling capacity of component and the controllability of deformation,
Greatly reduce the design difficulty of the deformable component with certain space constraint and complex-curved requirement；Meanwhile, using physics
Model spontaneous strain under restraining force effect carries out deformable component design, it is to avoid complex-curved cumbersome three-dimensional modeling mistake
Journey, is remarkably improved the design efficiency of deformable product.
Brief description of the drawings
Fig. 1 is the design flow diagram of deformable component model in the present invention.
Fig. 2 is the deformation process schematic diagram of deformable component model in specific embodiment of the invention 1.
Fig. 2 a are the deformation initialization schematic diagrames of deformable component model in specific embodiment of the invention 1.
Fig. 2 b are the deformation stage schematic diagrames of deformable component model in specific embodiment of the invention 1.
Fig. 2 c are that the deformation of deformable component model in specific embodiment of the invention 1 terminates schematic diagram.
Fig. 3 is the palm three-dimensional model diagram in specific embodiment of the invention 2.
Fig. 4 is the deformation process schematic diagram of deformable component model in specific embodiment of the invention 2.
Fig. 4 a are the deformation initialization schematic diagrames of deformable component model in specific embodiment of the invention 2.
Fig. 4 b are the deformation stage schematic diagrames of deformable component model in specific embodiment of the invention 2.
Fig. 4 c are that the deformation of deformable component model in specific embodiment of the invention 2 terminates schematic diagram.
Fig. 5 is the net shape schematic diagram of deformable component model in specific embodiment of the invention 2.
Fig. 6 is the pictorial diagram of vertical mouse in specific embodiment of the invention 2.
Specific embodiment
With reference to embodiments and its accompanying drawing is further non-limitingly described in detail to technical solution of the present invention.
A kind of deformable component Fast design method based on space constraint, comprises the following steps：
Step 1：According to the design requirement and assembly environment of product, the space constraint border of target element is extracted；
Step 2：Simplified mass spring model is set up, its particle is all distributed in model surface, and only adjacent
It is attached by spring between two particles；Deformable component is initialized in constraint space, by gradually incremental air pressure come
The free wxpansion of deformable component is simulated, and carries out Mechanical Analysis of Particles；The gravity and frictional force of particle are to realizing deformable group
Part is designed without practical significance, and its value is set as 0, therefore the main stress of particle is spring force, particle movement damping force and inside
Gas pressure；
Step 3：The equation of motion of particle is solved, Mass-spring Equation of Motion is carried out using Verlet integration methods
Numerical integration solve；
Step 4：Collision detection is carried out, deformable component is processed using the collision checking method based on AABB bounding volumetrees
With the collision problem between constraint space border, execution step 5 or step 6 are then gone to；
Step 5：Whether judgment models reach satisfied shape, and deformation simulative is terminated if satisfied, and deformation terminates；If discontented
Meaning then re-executes step 2；
Step 6：The volume of target element is calculated, judges whether to reach predetermined volume, deformed if reaching and terminate；If reaching
Less than then re-executing step 2.
The mass spring model of above-mentioned steps 2, the equation of motion of its system is equation below：
In formula, M is the mass matrix of system, and X is the locus of particle, and t is the time for increasing gas pressure, Fk、FdWith
FpThe respectively gentle body pressure matrix of the spring force matrix of particle system, damping force matrix；
If the spring between particle is preferable Hookean spring, Hooke's law is obeyed, and ignore camber of spring damping, with matter
Each connected spring of point effect all strong to the particle, it is assumed that have j, root by the adjacent particle that spring is connected with particle i
According to Hooke's law, act on the spring force on particle i and make a concerted effort to be expressed as formula：
In formula,For the spring force that particle i is subject to is made a concerted effort, E is the adjacent point set between particle i with spring connection,
kijIt is the spring rate between particle i and j, xiWith xjIt is particle i and positions of the j in time t,It is bullet between particle i and j
The original of spring is long；
The damping force being subject in particle movement is directly proportional to the movement velocity of particle, then damping force is expressed as formula：
In formula,For the damping force that particle movement is subject to；C is damped coefficient, and v is the movement velocity of particle i；
Act on the gas pressure on particle i and be equal to the gas that gas is produced on each tri patch adjacent with particle i
Body pressure sum；For perfect gas, according to Clausius-Clapeyron equations, the gas pressure being subject on particle i is represented
It is equation below：
In formula,It is the gas pressure that particle i is subject to, Tri is the tri patch collection for sharing particle i, AikIt is and particle i
The area of connected triangle k,It is the outer normal vector of tri patch；
The equation of motion of the solution particle of above-mentioned steps 3 is that ((t- Δs t) is respectively adopted t+ Δ t) with x by particle position x
Taylor's formula is launched, then obtain equation below：X (t+ Δs t)=2x (t)-x (t- Δ t)+M-1F[x(t),v(t)]Δt2；
In formula, (t+ Δs t) is respectively t and the (rate matrices of t+ Δ t) moment particle systems for v (t) and v；X (t) and x
(t+ Δs t) is respectively t and the (transposed matrix of t+ Δ t) moment particle systems；F [x (t), v (t)] is t particle-bullet
The matrix of making a concerted effort being subject to of spring system.
The algorithm steps of the collision detection of above-mentioned steps 4 are as follows：
Step 4.1：Deformable component is set up using Octree space partitioning method to be surrounded with the level on constraint space border
Tree construction；
Step 4.2：Simulated time step is performed, x (t+ Δ t), and to now deformable group are calculated according to x (t)
The Bounding Box of part is updated；
Step 4.3：To carrying out bounding box test for intersection between deformable component and constraint space border, find and interfere
Bottom bounding box pair；
Step 4.4：Bottom bounding box to interfering carries out collision detection of high precision to internal geometric units, until looking for
Go out all particles and triangular unit for colliding, then update particle position, speed and stress, display model.
In above-mentioned steps 4.4, after specific collision cell is found, to (particle position at t+ Δ t) moment is modified,
The coordinate representation equation below put after correction position：
In formula, Δ t is time step, and d is penetrated into the depth inside constraint space for particle, and (t+ Δs t) is matter for P (t) and P
Point P is in t and the (position of t+ Δs t).
The volume of the target element of above-mentioned steps 6 be calculated as by deformable component to triangle gridding dough sheet and coordinate
The discrete tetrahedron volume constituted between origin is integrated, so that the volume of target element is expressed as formula：
In formula, Vi1x、Vi1yAnd Vi1zThe three dimensional space coordinate of the particle i1 respectively on tri patch, Vi2x、Vi2yAnd Vi2z
The three dimensional space coordinate of the particle i2 respectively on tri patch, Vi3x、Vi3yAnd Vi3zParticle i3's respectively on tri patch
Three dimensional space coordinate, and arranged in counter clockwise direction around its exterior normal in these three particles.
Embodiment 1
According to above-mentioned deformation algorithm and flow, as shown in figure 1, carrying out deformation simulative system using VC++ program languages
Exploitation, set up based on mass spring model deformation simulative system；And figure is carried out by OpenGL shape libraries render, it is real
The deformation simulative of existing deformable component expansion.Prove that the deformable component based on space constraint proposed by the invention is quick with this
Method for designing is in the environment of with certain assembly constraint to the validity and feasibility of the design of deformable component.Specific steps are such as
Under：
Step 1：Extract the space constraint border of target element；
Step 2：Set up simplified mass spring model and analog parameter be set, object module is initialized to a bead,
Its triangle patch grids quantity is 3000；The target volume of deformable component is set to 110000cm3；Deformation simulative parameter is：
Spring constant ks=1000N/m, time step Δ t=0.01s, deformable assembly quality m=1kg, gas pressure increment Delta p=
1N/m2.In assembly space, in addition to deformable component, also show setting shape group really with simple geometry body surface including five
Part, as shown in Figure 2 a；
Increase object module internal gas pressure, makes its volume constantly expand, and force analysis is carried out to model particle, is touched
Hit detection and display model.Model other assemblies in by assembly space are constrained, and the shape of bead takes place change, such as
Shown in Fig. 2 b；
Step 3：Continue the internal gas pressure of increase target element model, the volume also constantly increase, meter therewith of model
Changeability assembly volume is calculated, deformation, net shape such as Fig. 2 c of object module are stopped after being finally reached set target volume
It is shown.
The deformation process schematic diagram of the deformable component model shown in Fig. 2 a to 2c can be seen that deformable component moulding
The acquisition of design is obtained by simulating the dilatancy process of balloon under class nature completely, it is not necessary to artificially done
In advance, and reached meet space it is non-interference on the premise of realize to assembly volume control effect.
Embodiment 2
According to above-mentioned deformation algorithm and flow, as shown in figure 1, carrying out deformation simulative system using VC++ program languages
Exploitation, set up based on mass spring model deformation simulative system；And figure is carried out by OpenGL shape libraries render, it is real
The deformation simulative of existing deformable component expansion.Prove that the deformable component based on space constraint proposed by the invention is quick with this
Method for designing is in the environment of with certain assembly constraint to the validity and feasibility of the design of deformable component.Specific steps are such as
Under：
Step 1：The space constraint border of target element is extracted, palm is obtained in natural relaxation shape by three-dimensional scanning device
Threedimensional model under state, as shown in Figure 3.Hand and desktop are defined as fixed constraint border, and remaining is supplemented according to design idea
Border forms closing space；
Step 2：Set up simplified mass spring model and analog parameter be set, object module is initialized to a bead,
As shown in fig. 4 a.Gas pressure inside increase bead model forces its dilatancy, as shown in Figure 4 b.And model particle is entered
Row force analysis, collision detection and display model；
Step 3：Continue the internal gas pressure of increase target element model, due to the pact of the compositions such as palm model and desktop
The limitation on beam border, model will progressively be deformed into reach and be satisfied with stopping deformation after shape, as illustrated in fig. 4 c.
The net shape of mouse deformable model obtained by method of the present invention is used as shown in figure 5, this is caused
Mouse user is possible to remain posture that is the most natural, loosening when long-time is using mouse, so as to reduce the tired of operation
Exhausted sense, vertical mouse pictorial diagram is as shown in Figure 6.
In sum, a kind of deformable component Fast design method based on space constraint proposed by the present invention, will be variable
Shape component is modeled as the flexible article with certain space volume, by giving suitable stress, deformation and constraints, makes
It dilatancy and is finally reached design requirement in virtual assembly environment；Strictly controlled using accurate collision checking method
The deformation process of model, can prevent deformable component from being interfered with other assemblies, so as to ensure assembling capacity and the change of component
The controllability of shape, greatly reduces the design difficulty of the deformable component with certain space constraint and complex-curved requirement；Together
When, using physical model, spontaneous strain carries out deformable component design under restraining force effect, it is to avoid complex-curved cumbersome
Three-dimensional modeling process, is remarkably improved the design efficiency of deformable product.
It is pointed out that above-described embodiment is only explanation technology design of the invention and feature, it is ripe its object is to allow
The personage for knowing technique will appreciate that present disclosure and implements according to this, can not limit protection model of the invention with this
Enclose.Any equivalent change or modification in accordance with the spirit of the invention, should all be included within the scope of the present invention.
Claims (6)
1. a kind of deformable component Fast design method based on space constraint, it is characterised in that comprise the following steps：
Step 1：According to the design requirement and assembly environment of product, the space constraint border of target element is extracted；
Step 2：Simplified mass spring model is set up, its particle is all distributed in model surface, and two only adjacent matter
It is attached by spring between point；Deformable component is initialized in constraint space, is simulated by gradually incremental air pressure
The free wxpansion of deformable component, and carry out Mechanical Analysis of Particles；The gravity and frictional force of particle set to realizing deformable component
No practical significance is counted, its value is set as 0, therefore the main stress of particle is spring force, particle movement damping force and internal gas
Pressure；
Step 3：The equation of motion of particle is solved, the number of Mass-spring Equation of Motion is carried out using Verlet integration methods
Value Integration Solving；
Step 4：Carry out collision detection, processed using the collision checking method based on AABB bounding volumetrees deformable component with about
Collision problem between beam space boundary, then goes to execution step 5 or step 6；
Step 5：Whether judgment models reach satisfied shape, and deformation simulative is terminated if satisfied, and deformation terminates；If dissatisfied
Re-execute step 2；
Step 6：The volume of target element is calculated, judges whether to reach predetermined volume, deformed if reaching and terminate；If not reaching
Then re-execute step 2.
2. the deformable component Fast design method based on space constraint according to claim 1, it is characterised in that：It is described
The mass spring model of step 2, the equation of motion of its system is equation below：
In formula, M is the mass matrix of system, and X is the locus of particle, and t is the time for increasing gas pressure, Fk、FdAnd FpPoint
Not Wei particle system spring force matrix, the gentle body pressure matrix of damping force matrix；
If the spring between particle is preferable Hookean spring, Hooke's law is obeyed, and ignore camber of spring damping, be connected with particle
All strong to the particle effect of each spring, it is assumed that have j by the adjacent particle that spring is connected with particle i, according to Hooke
Law, acts on the spring force on particle i and makes a concerted effort to be expressed as formula：
In formula,For the spring force that particle i is subject to is made a concerted effort, E is the adjacent point set between particle i with spring connection, kijFor
Spring rate between particle i and j, xiWith xjIt is particle i and positions of the j in time t,It is spring between particle i and j
Original is long；
The damping force being subject in particle movement is directly proportional to the movement velocity of particle, then damping force is expressed as formula：
In formula,For the damping force that particle movement is subject to；C is damped coefficient, and v is the movement velocity of particle i；
Act on the gas pressure on particle i and be equal to the gas pressure that gas is produced on each tri patch adjacent with particle i
Power sum；For perfect gas, according to Clausius-Clapeyron equations, the gas pressure being subject on particle i be expressed as
Lower formula：
In formula,It is the gas pressure that particle i is subject to, Tri is the tri patch collection for sharing particle i, AikIt is to be connected with particle i
The area of triangle k,It is the outer normal vector of tri patch；
3. the deformable component Fast design method based on space constraint according to claim 1, it is characterised in that：It is described
The equation of motion of the solution particle of step 3 is that ((t- Δs t) is respectively adopted Taylor's formula and carries out t+ Δ t) with x by particle position x
Launch, then obtain equation below：
X (t+ Δs t)=2x (t)-x (t- Δ t)+M-1F[x(t),v(t)]Δt2；
In formula, (t+ Δs t) is respectively t and the (rate matrices of t+ Δ t) moment particle systems for v (t) and v；X (t) and x (t+
Δ t) is respectively t and the (transposed matrix of t+ Δ t) moment particle systems；F [x (t), v (t)] is t Mass-spring system
The matrix of making a concerted effort being subject to of system.
4. a kind of deformable component Fast design method based on space constraint according to claim 1, it is characterised in that
The algorithm steps of the collision detection of the step 4 are as follows：
Step 4.1：Deformable component is set up using Octree space partitioning method and surrounds tree knot with the level on constraint space border
Structure；
Step 4.2：Simulated time step is performed, x (t+ Δ t), and to now deformable component are calculated according to x (t)
Bounding Box is updated；
Step 4.3：To carrying out bounding box test for intersection between deformable component and constraint space border, the bottom for interfering is found
Layer bounding box pair；
Step 4.4：Bottom bounding box to interfering carries out collision detection of high precision to internal geometric units, until finding out
There are the particle and triangular unit for colliding, then update particle position, speed and stress, display model.
5. the deformable component Fast design method based on space constraint according to claim 4, it is characterised in that：Institute
In stating step 4.4, after specific collision cell is found, to (particle position at t+ Δ t) moment is modified, after correction position
The coordinate representation equation below of point：
In formula, Δ t is time step, and d is penetrated into the depth inside constraint space for particle, and (t+ Δs t) is particle P for P (t) and P
In t and the (position of t+ Δs t).
6. the deformable component Fast design method based on space constraint according to claim 1, it is characterised in that：The step
The volume of rapid 6 target element be calculated as by deformable component between triangle gridding dough sheet and the origin of coordinates constitute from
Dissipate tetrahedron volume to be integrated, so that the volume of target element is expressed as formula：
In formula, Vi1x、Vi1yAnd Vi1zThe three dimensional space coordinate of the particle i1 respectively on tri patch, Vi2x、Vi2yAnd Vi2zRespectively
It is the three dimensional space coordinate of the particle i2 on tri patch, Vi3x、Vi3yAnd Vi3zThe three-dimensional of the particle i3 respectively on tri patch
Space coordinates, and arranged in counter clockwise direction around its exterior normal in these three particles.
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| CN201710032353.3A CN106874563A (en) | 2017-01-16 | 2017-01-16 | A kind of deformable component Fast design method based on space constraint |
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| CN111932597A (en) * | 2020-10-09 | 2020-11-13 | 江苏原力数字科技股份有限公司 | Interactive self-penetrating grid deformation method based on proxy geometry |
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