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Computer-Generated Watercolor Cassidy J. Curtis Sean E. Anderson Joshua E. Seims Kurt W. Fleischer David H. Salesin

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Outline Introduction Related work Background Overview Watercolor simulation Rendering Applications Results Conclusion

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Introduction Various artistic effects of watercolor

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Related work Simulating artists’ traditional media and tools –Watercolor : [David Small 1991] –Sumie : [Guo and Kunii 1991] Commercial package –Fractal Design Painter

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Background Properties of watercolor –Watercolor paper –Pigment –Binder –Surfactant

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Background Watercolor Effects a) dry-brush b) Edge darkening c) Backruns d) granulation and separation of pigments e) Flow patterns f) color glazing

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Overview Computer-generated watercolor 1. Fluid (and pigment) simulation for each glaze 2. Rendering Glaze: physical properties, area

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Fluid simulation Three-layer model

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Fluid simulation Paper Generation –Height field model ( 0 < h < 1 ) –Based on pseudo-random process –Fluid capacity c : proportional to h

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Fluid simulation Main loop Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments For each time step

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Fluid simulation Main loop Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments For each time step

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Moving water conditions of water 1. To remain within the wet-area mask 2. To flow outward into nearby region 3. To be damped to minimize oscillating waves 4. To be perturbed by the texture of the paper 5. To be affected by local changes 6. To present the edge-darkening effect Navier-Stoke Eq. Viscous drag k Paper slope h Mass conserv.Flow outward Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Configuration –Staggered grid i,j Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Updating the water velocities –Governing Equation (2D Navier-Stoke Eqn.) Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Derivation of Navier-Stoke Eqn.(1/5) –Basic Eqn.: –For unit volume: Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Derivation of Navier-Stoke Eqn.(2/5) –Two kind of measurements fluid solid Control volume Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Derivation of Navier-Stoke Eqn.(3/5) –Eulerian view Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Derivation of Navier-Stoke Eqn.(4/5) –Governing Eq.: –Forces: Gravity: Viscosity: Pressure: Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Derivation of Navier-Stoke Eqn.(5/5) –Navier-Stoke Eqn. –For 2D case, Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Updating the water velocities –Numerical integration for u Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Updating the water velocities –Applying paper slope effect: –Applying Drag Force: Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Mass conservation (1/3) –Divergence free condition Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Mass conservation (2/3) –Relaxation (iterative procedure) Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Mass conservation (3/3) –Relaxation (iterative procedure) Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Edge darkening –To flow outward Remove some water at the boundary Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Edge darkening Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments drywet 0 0 00 0 0 0 0 0 1 1 11 1 1 1 1 1 M.1 0.4 0 0.6 1.9 1 1 M’ 0 0 00 0 0 0 0 0.4 0.1 0 0 (1-M’)M

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Fluid simulation Main loop Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments For each time step

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Fluid simulation Moving Pigments –To move as specified by the velocity field u,v Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Moving Pigments –To move as specified by the velocity field u,v Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Main loop Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments For each time step

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Fluid simulation Transferring Pigments –Adsorption and desorption Adsorption Desorption Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Main loop Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments For each time step

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Fluid simulation Backruns –Diffusing water through the capillary layer Spreading slowly into a drying region Transfer water to its dryer neighbors until they are saturated Applying Capillary Flow Moving Water Moving Pigments Transferring Pigments

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Fluid simulation Drybrush effect –By excluding any lower pixel than threshold

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Rendering Optical properties of pigments –Optical composition – subtractive color mixing

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Rendering Optical properties of pigments –Kubelka-Munk (KM) Model –To compute Reflectance R and Transmittance T using K and S unit length absorbed K backscattered S

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Rendering Optical properties of pigments –Kubelka-Munk (KM) Model

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Rendering Optical properties of pigments –Kubelka-Munk (KM) Model –For multiple layers

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Rendering Optical properties of pigments –Kubelka-Munk (KM) Model We need S and K values Make user choose them intuitively

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Rendering Optical properties of pigments –User selects Rw and Rb

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Rendering Optical properties of pigments –User selects Rw and Rb

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Applications 1. Interactive painting with watercolors 2. Automatic image “watercolorization” 3. Non-photorealistic rendering of 3D models

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Applications 1. Interactive painting with watercolors

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Applications 2. Automatic image “watercolorization” –Color separation –Brushstroke Planning

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Applications 2. Automatic image “watercolorization” –Color separation Determine the thickness of each pigment by brute- force search for all color combinations

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Applications 2. Automatic image “watercolorization” –Brushstroke planning

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Applications 3. Non-photorealistic rendering of 3D models –Using “photorealistic” scene of 3D model

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Results

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Conclusion Various artistic effects of watercolor –Water and pigment simulation –Pigment Rendering Application –Interactive system –Automatic “watercolorization” of 2D and 3D

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Further work Other effects –Spattering and drybrush Automatic rendering –Applying automatic recognition Generalization –Integration of Wet-in-wet and backruns Animation issues –Reducing temporal artifacts

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