Modeling Of The 3D Brush And The Control Method Of Virtual Haptic Painting

Product appearance design plays an increasingly important role in the conceptual design stage of modern industrial components or consumer products,both at the enterprise level and at the level of ordinary consumers.Conceptual design of product appearance,including product shape design and aesthetic decoration of product surface,is usually accomplished by computer aided industrial design.For designers,CAID has become an effective way to quickly complete the innovative design of industrial products and display product functions.Traditional CAID uses global texture mapping method to realize the transformation from two-dimensional graphics to three-dimensional model outer surface,so as to achieve the aesthetic decoration of three-dimensional product outer surface.However,the process of mapping and transforming from 2D graphics to 3D objects surface can easily cause uncontrollable distortion and aliasing of the original 2D graphics,and the process of applying texture mapping is cumbersome,and easy to consume too much computer resources.In the innovative design of product appearance,Designers inspiration plays a very important role.Texture mapping technology needs to map 2D graphics to the 3D surface.The process is rigid,which prevents designers from freely capturing design inspiration.With the development of the virtual painting technologies with specific style,such as painting and calligraphy,more and more attention has been paid to the technology of direct painting on the 3D surface.So,a new haptic painting method on the 3D surface based on real-time force feedback technology is proposed in this paper.The main research contents are as follows:(1)The influence mechanism of force on the bending deformation of brush in the actual painting process is analyzed.The relationship between the applied moment,the humidity of brush head,the friction force of painting surface and the real-time deformation of brush is studied.A new physical model of force feedback based on variable stiffness and elastic-plastic is proposed.Firstly,the mechanical model of the brush is constructed by using the elastic-plastic bending spring model,and the relationship between the force of the brush and the bending displacement and the rotation displacement of the brush is simulated.The corresponding friction coefficient is determined according to the material properties of the rendered object surface,and the dynamic friction between the brush and the virtual surface is calculated by combining the reaction of the painting surface to the brush head obtained by solving the bending deformation differential equation.The simulation model of the bifurcation of the brush head is constructed by the force of the pen rod,the surface friction force,the speed of the brush moving and the humidity of the brush head.A virtual 3D brush geometry model is constructed by decomposing the brush center skeleton and the skin triangular mesh.The bending deformation of the central skeleton of the brush and the corresponding surface deformation of the brush head are simulated in real time by using the improved three-dimensional mesh deformation technology driven by the mean skeleton.The dynamic control of the bending deformation of the brush by the force is realized.(2)Research on control method of virtual basic 2D brush stroke painting.First of all,according to the relationship between the force exerted on the brush and the deformation of the brush in the process of moving the brush,a mathematical model of spatial relationship between virtual 3D brush and virtual plane is established when bending deformation occurs at single sampling time.Combining with real brush pattern,rational B-spline technique is used to fit the stroke shape similar to "raindrop".The users use the stylus of the force feedback device to control the brush behavior,and the brush strokes are superposed along the direction of brush movement to generate various styles of 2D brush stroke effects.(3)Research on the control method of special stroke effect.①Based on KM color optics theory,a new method for color simulation of ink pigments in virtual rendering process is proposed.Firstly,the basic differential equation of KM optical theory is used to derive the corresponding reflection coefficient and transmission coefficient formulas when the thickness of any pigment is D.Then,based on the reflection coefficient and transmission coefficient of pigments,a single color simulation algorithm,a multi-color mixing simulation algorithm and a multi-layer color overlay simulation algorithm are constructed.Finally,the conversion method from the reflectivity of the three color channels of the paint layer to the color brightness value(R,G,B)is established,and the storage of the rendering results of the virtual three-dimensional object surface is realized.②A novel three-dimensional rendering simulation model for the transport and diffusion of ink pigments is proposed.Firstly,the diffusion mechanism of two-dimensional ink pigments was studied,and a parameterized rice paper fiber model based on paper elements was constructed.Then,the simulation model of ink pigments transmission process between brush and rice paper surface was established.Based on the second law of unsteady diffusion,the differential equation of diffusion motion of water particles in water-ink mixture on rice paper surface was established,and the real-time diffusion behavior of water particles on rice paper surface was simulated.The differential equation of convection and diffusion of pigments was established by introducing dynamic diffusion coefficient,and the diffusion behavior of pigments in water-ink mixture on rice paper surface was simulated.Similarly,based on Fick’s second diffusion law,a simulation model of the diffusion process of ink pigment particles in the brush head was established.We establish the evaporation equation based on diffusion theory,and add the influence of atmospheric pressure in the environment on the evaporation of water.The differential equations of water evaporation on the brush head and the rice paper are established respectively,which can effectively simulate the evaporation process.Finally,the "deposition rate" of pigments was put forward,and the semi-empirical formula for calculating the deposition rate was given to simulate the "granular" phenomenon of the deposited pigments.(4)Research on real-time haptic painting technology of 3D brush stroke on virtual object surface.The real-time,efficient and accurate collision detection between virtual brush and virtual object surface is guaranteed by using optimized hybrid octree hierarchical bounding box technology and multi-threaded dynamic task allocation parallel computing technology.A"weighted average distance" algorithm is used to simulate the tactile force between the brush head and the virtual object surface.The tactile force between the brush head and the 3D object surface is simulated when the brush head touches the three-dimensional rendering surface.we establish the minimum bounding sphere of the bending brush based on a sphere expansion algorithm.The average normal and spatial positions of the virtual projection plane are calculated based on the minimum bounding sphere.A local real-time mapping is studied,which can map 2D strokes onto the surface of 3D objects in real time and obtain virtual 3D strokes.By controlling the painting force,the virtual 3D brush strokes of different sizes and shapes obtained at each sampling time are superimposed along the drawing direction to obtain the virtual three-dimensional brush strokes.In virtual rendering,artists can "intentionally"control the virtual rendering behavior through real-time tactile and visual feedback to form the desired painting effect of 3D surface and improve the reality of the 3D painting process.(5)Real time optimization of 3D interactive painting system.Firstly,the rules of setting the response frequency of force feedback in haptic painting are given.Secondly,the influence of the dynamic sampling time of the brush on the real-time performance of the painting system is considered.By optimizing the dynamic sampling time Δt of the virtual brush and integrating multi-threaded parallel processing technology,the overall real-time performance of the painting system are effectively improved.