(full 3D hemispherical scattering measurements ->)
1. The primary specular highlight continues all the way around the
hair, while the secondary highlight is confined to the side of the hair
toward the source.
2. A pair of large out-of-plane peaks, or glints, are present, and as
the incidence angle increases the peaks move closer to the incidence
plane, eventually merging and disappearing.
3. The scattering distribution depends on the angle of rotation of the
hair fiber about its axis. (Because hair fibers are not generally
circular in cross section.)
4. Three trasport modes are derived: surfacce reflection, transmission, and internal reflection.
2 Fibers 2.1 Hair fibers and fiber scattering
The fiber is modeled as a dielectric cylinder covered with tilted
sacles (the cuticle) and with a pigmented interior (the cortex).
The cones of the R and TRT components shift in opposite directions,
causing them to separate into two visually distinguishable highlights.
(The R highlight is white and the TRT highlight is colored.)
2.2 Scattering
The bidirectional scattering function S for a fiber (different from the bidirectional reflection distribution function f_r for a surface):
The scattering integral (the curve intensity scattered from an infinitesimal length of fiber):
The presence D in this equation (1) indicates that
a thick fiber intercepts more light, and therefore appears brighter from a distance, than a thin fiber.
3 Scattering measurements 3.1 Incidence plane
As the scattering angle increases, the secondary highlight fades out, while the primary highlight maintains more constant amplitude. Both peaks maintain approximately constant width.
The equal-angle peak
3.2 Normal plane
The hair has a 180 degree rotational symmetry and is bilaterally symmetric in cross section.
The evolution of the peaks as the fiber roatates appears similar to the internal reflection from a transparent elliptical cylinder.
3.3 3D hemispherical measurements 3.3.1 Changes in glints with angle of incidence
The azimuth at which the glints occur changes as a function of incidence angle, with the glints moving toward the incidence plane as the incidence moves from normal to grazing.
3.3.2 Hemispherical scattering
3.4 Summary
4 Theory of scattering from fibers 4.1 Scattering from cylinders
Walt Disney Features Animation EVASION-INRIA, Grenoble, France Rhythm & Hues Studios Cornell University EVASION/INRIA & INP Grenoble, France University of North Carolina at Chapel Hill
I. A. Hair Modeling Overview
hair modeling - hairstyling / hair simulation / hair rendering hairstyling: modeling the shape of the hair - geometry, density, distribution, orientation hair simulation: dynamic motion of hair - collision, mutual interactions hair rendering: visual depiction of hair - color, shadows, light scattering, transparency, anti-aliasing
ref. Magnenat-Thalmann
- geometric complexity and thin nature of an individual strand coupled with the complex collisions and shadows that occur among the hairs
GPU
I. B. Applications and Remaining Problems
cosmetic product entertainment industry (feature animation) interactive systems (virtual environments, videogames)
II. HAIRSTYLING II. A. Hair Structural and Geometric Properties
hair types - Asian / African / Caucasian - Asian: smooth, regular, a circular corss-section - African: irregular, an elliptical cross-section - Caucasian: ranged from smooth to curly
Visual styling techniques are for applications that desire a visually-prausible solution to match the final results with the appearance of real-world hair.
II. B. Attaching Hair to the Scalp
1) 2D Placement : spherical mapping of 2D map to the 3D contour of the scalp * TY Kim - 2D space defined by the two parametric coordinates of the patch wrapped interactively over the head model * Bando - harmonic mapping, compensation based on a Poisson disc distribution
2) 3D Placement : selecting triangles defined the scalp interactively
3) Distribution of Hair Strands on the Scalp : uniform distribution over the scalp * the user's painting local hair density as color levels and further characteristics such as length or curliness
ref. B. Hernandez & I. Rudomin, <Hair Paint>, Computer Graphics International (CGI), June 2004, pp. 578-581
II. C. Global Hair Shape Generation
1) Geometry-Based Hairstyling : a parametric representation of hair in the form of trigonal prisms or generalized cylinders a) Parametric Surface: A patch of a parametric surface such as a NURBS surface("hair strips") are given a location on the scalp, an orientation, and weighting for knots to define a desired hair shape. * U-shape * Thin Shell Volume (TSV) * key hair curves generated along the isocurves of the NURBS volume b) Wisps and Generalized Cylinders: The positioning of one general space curve serves as the center of a radius function defining the cross-section of a generalized cylinder ("a hair cluster"). c) Multi-resolution Editing: A hierarchy of generalized cylinders allows users to select a desired level of control in shape modeling.
2) Physically-based Hairstyling a) The Cantilever Beam: A cantilever beam is defined as a straight beam embedded in a fixed support at one end only. Gravity and extra-forces need to be applied to the strand. b) Fluid Flow: The idea that static hair shapes resemble snapshots of fluid flow around obstacles. c) Styling Vector and Motion Fields: Given a global field generated by superimposing procedurally defined vector field primitives, hair strands are extracted by tracing the field lines of the vector field. Hair deformation is computed by using the previous algorithm applied on the modified vector field. (Three types of constraints: point / trajectory / direction)
3) Generation of Hairstyles from Images : the automatic reconstruction of hair from imgaes a) Hair Generation from Photographs: Building a 3D hair volume from various viewpoints of the subject's hair is for simple hairstyles. b) Hair Generation from Sketches: In a sketch-based system dedicated to modeling cartoon hairstyles, Curves representing clusters of hair are generated between silhouette surface and the scalp.
4) Evaluation
II. D. Managing Finer Hair Properties
1) Details of Curls and Waves - a class of trigonometric offset functions with rabdin terms - a breakaway behaviour from the fluid flow based on a probability function - the degree of similarity among the master strands controlled by a length distribution, a deviation radius function and a fuziness value * a Markov chain process * a Gibbs distribution * the Kirchhoff model (: a mechanically accurate model for static elastic rods)
2) Producing Hair Volume - for hair self-collisions, hair can be viewed as a continuous medium - the idea that hair strands with pores at higher latituds on the head cover strands with lower pores - a hair-head collision detection & response algorithm * a quasi-static head
3) Modeling Styling Products and Water Effects - A styling force is used to enable hairstyle recovery as the hair moves due to external force or head movement. (1)The desire is to retain the deformed hairstyle rather than returning to the initial style. (2)Breakable static links or dynamic bonds can be used to capture hairstyle recovery by applying extra spring forces between nearby sections of hair (to mimic the extra clumping of hair created by styling products). - Using a dual-skeleton model for simulating the stiffness of hair motion, separated spring forces can be used to control the bending of hair strands versus the stretching of curls. - " As water is absorbed into hair the mass of the hair increases uip to 45%, while its elasticity modulus decreased by a factor of 10." And the volume of the hair decreases due to the bonding nature of water. * Young's modulus of each fiber - An interactive virtual hairstyling system introduced by Ward et al.
ref. K. Ward, N. Galoppo, M. C. Lin <Modeling hair influenced by water and styling products>, International Conference on Computer Animation and Social Agents (CASA), May 2004, pp. 207-214 K. Ward, N. Galoppo, M. Lin <Interactive virtual hair salon>, PRESENCE: Teleoperators & Virtual Environments (to appear), 2007
III. HAIR SIMULATION III. A. The Mechanics of Hair
- The irregular surface of individual hair strands causes anisotropic friction inside hair, with an amplitude (that strongly depends on the orientation of the scales and of the direction of motion). - Hair-hair friction results in triboelectricity. - The more intricate the hair's geometry is, the less degrees of freedom it has during motion.
III. B. Dynamics of Individual Hair Strands
1) Mass-Spring Systems : A single hair strand is modeled as a set of particles connected with stiff springs and hinges.
2) One Dimensional Projective Equations : The statics of a cantlever beam is simulated to get an initial plausible configuration of each hair strand. Then, each hair strand is considered as a chain of rigid sticks.
3) Rigid multi-body serial chain : Each hair strand can be represented as a serial, rigid, multi-body open chain using the reduced or spatial coordinates formulation, in order to keep only the bending and twisting degrees of freedom of the chain. * Articulated-Body Method * DOF * multi-pass forward dynamics algorithm
4) Dynamic Super-Helices * Kirchhoff theory for elastic rods : The curvatures and the twist of the rod are assumed to remain constant over each predefined piece of the rod. As a result, the shape of the hair strand is a piecewise helix, with a finite number of degrees of freedom. This model is then animated using the princiles of Lagrangian mechanics, accounting for the typical nonlinear behavior of hair, as well as for its bending and twisting deformation modes.
5) Handling external forces
ref. D. W. Lee & H. S. Ko <Natural hairstyle modeling and animation>, Graphical Models, vol. 63, no. 2, pp. 67-85, March 2001
[39]
6) Evaluation (Table II 삽입!)
III. C. Simulating the Dynamics of a Full Hairstyle
detection and resonse => computing hair contacts and collisions
1) Hair as a Continuous Medium : hair as an anisotropic continuous medium a) Animating Hair Using Fluid Dynamics: Interaction dynamics, including hair-hair, hair-body, and hair-air interactions, are modeled using fluid dynamics. Individual hair strands are kinematically linked to fluid particles in their vicinity. The density of the hair medium is defined as the mass of hair per unit of volume occupied. The pressure and viciosity represent all of the forces due to interactions to hair strands. Hair-body interactions are modeled by creating boundary fluid particles around solid objects. A fluid particle, or Smooth Particle Hydrodynamics (SPH), exerts a force on the neighboring fluid particles basedd on its normal direction. The viscous pressure of the fluid, which is dependent on the hair density, accounts for the frictional interactions between hair strands. b) Loosely Connected Particles: Each particle represents a certain amount of hair material which has a local orientation (the orientation of a particle being the mean orientation of every hair strand covered by the particle). Initially, connected chains are setteld between neighboring particles being aligned with local hair orientation: two neighboring particles having similar directions and being aligned with this direction are linked. -> breakable links between close particles c) Interpolation between Guide Hair Strands: Using multiple guide hair strands for the interpolation of a strand alleviates local clustering of strands. A collision among hair strands is detected by checking for intersections between two hair segments and between a hair vertex and a triangular face. d) Free Form Deformation (FFD): A mechanical model lis defined for a lattice surrounding the head. The lattice is then deformed as a particle system and hair strands follow the deformation by interpolation. * metaball
2) Hair as Disjoint Groups : to capture local discontinuities observed inside long hair during fast motion a) Real-time Simulation of Hair Strips: The projective angular dynamics method is applied to the control point mesh of the NURBS surface. The strips of texture-mapped hair are simulated using a mass-spring model and 3D morphing. b) Simulation of Wisps: During motion, the shape of a wisp is approximated by parabolic trajectories of fictive particles initially located near the root of each wisp.
III. D. Multi-resolution Methods
1) Level-of-Detail Representations : Three different levels of detail (LODs) for modeling hair - individual strands, clusters and strips represented by subdivision curves, subdivision swept volumes, and subdivision patches. The family of swept shpere volumes (SSVs) as bounding volumes encapsulates the hair.
2) Adaptive Clustering : The Adaptive Wisp Tree (AWT) represents at each time step the wisps segments of the hierarchy that are actually simulated (called active segments). The AWT dynamically splits or merges hair wisps while always preserving a tree-like structure.
IV. HAIR RENDERING IV. A. Representing Hair for Rendering
explicit models - line or triangle-based renderers volumetric models - volume renderers, or rendering algorithms
1) Explicit Representation - curved cylinders / trigonal prisms with three sides / ribbon-like connected triangle strips / tessellating a curved hair geometry into polygons
2) Implicit Representation - volumetric textures (texels) / the cluster hair model
IV. B. Light Scattering in Hair
: The first requirement for any hair rendering system is a model for the scattering of light by individual fibers of hair.
1) Hair Optical Properties - A hair fiber is composed of three structures: the cortex, the cuticle, and the medulla. - A hair is composed of amorphous proteins that act as a transparent medium with an index of refraction (refractive index=1.55). - The cortex and medulla contain pigments that absorb light, often in a wavelength-dependent way; these pigments are the cause of the color of hair.
2) Notation and Radiometry of Fiber Reflection Because fibers are usually treated as one-dimensional entities, light reflection from fibers needs to be described somewhat differently from the more familiar surface reflection.
Light scattering at a surface is conventionally described using the bidirectional reflectance distribution function (BRDF). The BRDF gives the density with respect to the projected solid angle of the scattered flux that results from a narrow incident beam. It is defined as the ration of surface radiance (intensitiy per unit projected area) exiting the surface in direction w_r to surface irradicance (flux per unit area) falling on the surface from a differential solid angle in the direction w_i:
The scattering function f_s for a fiber is "the ratio of curve radiance (intensity per unit projected length) exiting the curve in direction w_r to curve irradiance (flux per unit length) falling on the curve from a differential solid angle in the direction w_r."
The curve radiance due to illumination from an incoming radiance distribution
ref. S. Marschner, H. W. Jensen, M. Cammarano, S. Worley, and P. Hanrahan <Light scattering from human hair fibers>, ACM Transactions on Graphics, vol. 22, no. 3, pp. 780-791, July 2003, proceedings of ACM SIGGRAPH 2003
Curve irradiance measures the radiant power intercepted per unit length of fiber and therefore increases with the fiber's width.
=> Given two fibers with identical properties but different widths, the wider fiber will produce a brighter curve in a rendered image because the wider fiber intercepts more incident light. This definition is consistent with the behavior of real fibers: very fine hairs do appear fainter when viewed in isolation.
Light transmitted through a smooth cylinder will emit on the same cone as the surface reflection, no matter what sequence of refractions and internal reflections it may have taken.
4) Measurements of Hair Scattering There are two specular peaks, one on either side of the specular direction, and there is a sharp ture specular peak that emerges at grazing anles.
5) Models for Hair Scattering Fermat's Principle: A light ray, in going between two points, must
traverse as optical path length which is stationary with respect to variations of the path.
Fresnel factor Fresnel diffraction or near-field diffraction is a process of diffraction which occurs when a wave passes through an aperture
and diffracts in the near field, causing any diffraction pattern
observed to differ in size and shape, relative to the distance. It
occurs due to the short distance in which the diffracted waves propagate.
6) Light Scattering on Wet Hair When objects become wet thet typically appear darker and shinier. As hair becomes wet, a thin film of water is formed around the fibers, forming a smooth, mirror-like surface on the hair. This smoother surface creates a shinier appearance of the hair due to increased specular reflections. Light rays are subject to total internal reflection inside the film of water around the hair strands, contributing to the darker appearance wet hair has over dry hair. Water is absorbed into the hair fiber, increasing the opacity value of each strand leading to more aggressive self-shadowing.
IV. C. Hair Self-Shadowing and Multiple Scattering
Self-shadowing creates crucial visual patterns that distinguish one hairstyle from another.
1) Ray-casting through a Volumetric Representation
2) Shadow Maps The shadow map is a depth image of hair rendered from the light's point of view. Each point of be shadowed is projected onto the light's camera and the point's depth is checked against the depth in the shadow map.
The transmittance function accounts for two important properties of hair. Fractional Visibility: If more hair fibers are seen along the path from the light, the light gets more attenuated (occluded), resulting in less illumination (shadow). Translucency
2) Interactive Volumetric Rendering > hair modeling as a set of connected particles (<= fast cloud rendering techniques) > accumulating transmittance values through a light-oriented voxel grid (-> interactive results for animated hair)
3) Graphics Hardware Graphics processor units (GPUs) languages such as Cg
V.
> physically-based realism (for cosmetic prototyping) > visual realism with a high user control (for feature films) > computations acceleration (for virtual environments and videogaes)
V. A. Hairstyling
- haptic techniques for 3D user input
V. B. Animation
V. C. Rendering
- simulating accurate models for both the scattering of individual hair fibers - the computations of self-shadows at interactive rates
fidelity (n) 원래 것과 똑같음, 박진성(迫眞性) erratic (adj) 산만한 on the fly: 작동/활동 중에 intricacy (n) 복잡함 -> (adj) intricate scalp (n) 두피 bangs (n) (단발의) 앞머리 braids (n) 땋은 머리 wisp (n) 한 줌 cantilever (n) 외팔보 pore (n) 털구멍 vortex (n) 소용돌이 heuristic (n) 발견적 방법 cumbersome (adj) 방해가 되는 facilitate (vt) (사물이 일을) 용이하게 하다 bun (n) (여성 뒷머리의) 쪽 perturb (vt) 교란하다 elongation (n) 연장(선) triboelectric (adj) [전기] 마찰 전기의 <- (n) triboelectricity articulate (v) (뼈를) 관절로 잇다 order of magnitude: 어떤 수치에서 그 10배까지의 범위 vicinity (n) 근처 voxel (n) [컴퓨터] (입체 화상을 구성하는) 3D 화소(畵素) auxiliary (adj) 보조의 dampen (v) 축축하게 하다 fictive (adj) 상상의 dissipative (adj) [물리] 에너지가 흩어지는 empiric = empirical (adj) 경험주의의 occlude (v) (구멍, 틈새를) 막다 tessellate (vt) (방바닥, 포장도로를) 바둑판 모양으로 만들다 cortex (n) 피층(皮層), 피질(皮質) medulla (n) 모수(毛髓) amorphous = formless pigment (n) [생물] 색소(色素) corollary (n) <문어> 추론, [수학] 계(系) graze (v) 가볍게 닿으며 지나가다 lobe (n) 둥근 돌출부 preliminary (adj) 예비적인 caustic (adj) [광학] 화선(화면)의 attenuate (v) 희박해지다 occlude (v) (구멍, 틈새를) 막다 haptic (adj) 촉각의
<A Self-Shadow Algorithm for Dynamic Hair using Density Clustering>
Tom Metens, Philippe Bekaert, Frank Van Reeth (Expertise Centre for Digital Media, Limburgs Universitair Centrum) Jan Kautz (CSAIL, Massachusetts Institute of Technology)
<A Simple, Efficient Method for Realistic Animation of Clouds>
Yoshinori Dobashi & Tsuyoshi Okita, Hiroshima City University Kazufumi Kaneda & Hideo Yamashita, Hiroshima University Tomoyuki Nishita, University of Tokyo
<An Integrated System for Modeling, Animating and Rendering Hair>
Agnes Daldegan & Nadia Magnenat Thalkmann, MIRALab, University of Geneva Tsuneya Kurihara, Central Research Laboratory, Hitachi, Ltd. Daniel Thalmann, Computer Graphics Lab, Swiss Federal Institute of Technology
Hair is a filamentous outgrowth of dead cells from skin, found only on mammals.
cf. Trichocytes : the specialized epithelial cells from which the highly mechanically resilient tissues hair and nail are formed. Epithelium : In biology and dermatology, a tissue composed of a layer of cells.
cf. A pigment is a material that changes the color of light it reflects as the result of selective color absorption. This physical process differs from fluorescence, phosphorescence, and other forms of luminescence, in which the material itself emits light. Many materials selectively absorb certain wavelengths
of light. Materials that humans have chosen and developed for use as
pigments usually have special properties that make them ideal for
coloring other materials. (...) Pigments, unlike fluorescent or phosphorescent substances, can only subtract wavelengths from the source light, never add new ones.
stereo viewing with left and right versions of the front and back bufferes
cf. stereo vision Stereoscopic depth is the sensation of depth that emerges from the
fusion of the two slightly different projections of the world on the
two retinas.
Advanced Graphics Programming Techniques Using OpenGL In August, this course was presented at the 1999 SIGGRAPH Conference in Los Angeles, California. The course demonstrated advanced techniques and concepts for programming with OpenGL.
Readership: Professional game and game engine developers; real-time graphics and simulation developers; creators of movie special effects; computer graphics, geometric modeling, CAGD, animation, and visualization programmers and researchers pertaining to all applications of practical, artistic, entertainment, medical, military, manufacturing etc. products.
Series: The Morgan Kaufmann Series in Computer Graphics
ISBN: 978-1-55860-848-1
ISBN10: 1-55860-848-6 Book/Hardback
Measurements: 7 3/8 X 9 1/4 in
Pages: 712 Imprint: Morgan Kaufmann
Publication Date: 2 December 2002
Price: £83.95
Because it was important to achieve a photorealistic look for various types of fur (e.g. long, short, wet) and at extreme close-ups, we opted to model each strand of hair using a simple spline-based geometric model that incorporates specialized lighting and self-shadowing methods.
A flattened
representation of the self-shadowing model we use.
The types of non-uniformities that can cause scattering, sometimes known as scatterers or scattering centers,
are too numerous to list, but a small sample includes particles,
bubbles, droplets, density fluctuations in fluids, defects in
crystalline solids, surface roughness, cells in organisms, and textile
fibers in clothing.
multiple scattering The main difference between the effects of single and multiple
scattering is that single scattering can usually be treated as a random
phenomenon and multiple scattering is usually more deterministic. (Single scattering is therefore often described by probability distributions. With multiple scattering, the randomness of the interaction tends to be
averaged out by the large number of scattering events, so that the
final path of the radiation appears to be a deterministic distribution
of intensity as the radiation is spread out. The description of scattering and the distinction between single and multiple scattering are often highly involved with wave-particle duality.)
2p Isotropy (the opposite of anisotropy) is the property of being independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.
Albedo is the ratio of reflected to incident electromagnetic radiation. It is a unitless measure indicative of a surface's or body's diffuse reflectivity.
Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i.e., clockwise) in astronomy and geodesy and from the south toward the west (i.e., clockwise) in surveying. It is usually expressed in degrees. Azimuth is also terms used in mining for a similar, but slightly different angle: azimuths and meridian angles are used to name any angle measured clockwise from any meridian.
3p solid angleΩ, that an object subtends
at a point is a measure of how big that object appears to an observer
at that point. For instance, a small object nearby could subtend the
same solid angle as a large object far away. The solid angle is
proportional to the surface area, S, of a projection of that object onto a sphere centered at that point, divided by the square of the sphere's radius, R. (Symbolically, Ω = k S/R², where k is the proportionality constant.) A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle.
(the outgoing radiance) = (the scattering function) * (the incident light distribution)
Monte Carlo integration is numerical quadrature using pseudorandom numbers. That is, Monte Carlo integration methods are algorithms for the approximate evaluation of definite integrals, usually multidimensional ones. The usual algorithms evaluate the integrand at a regular grid. Monte Carlo methods, however, randomly choose the points at which the integrand is evaluated. The traditional Monte Carlo algorithm distributes the evaluation points uniformly over the integration region. Adaptive algorithms such as VEGAS and MISER use importance sampling and stratified sampling techniques to get a better result.
(Random sampling of the region may not uncover all the important features
of the function, resulting in an underestimate of the error.)
ref. <A conceptual model of the dehydration of air due to freeze-drying
by optically thin, laminar cirrus rising slowly across the tropical
tropopause>
Eric J. Jensen, Leonhard Pfister, Andrew S. Ackerman, and Azadeh Tabazadeh
NASA Ames Research Center, Moffett Field, California
Owen B. Toon
University of Colorado, Laboratory for Atmospheric and Space Physics, Boulder, Colorado
Willian T. Reeves <Particle Systems—a Technique for Modeling a Class of Fuzzy Objects>, ACM Transactions on Graphics, Vol.2, no.2, April 1983, Page 91-108
The model definition is procedural and is controlled by random numbers.
efficiency of human design time (to obtain a highly detailed model)
ability to adjust the level of detail (to suit a specific set of viewing parameters)
fractal surfaces
It is easier to model "alive" objects changing form over a period of time.
keywords: image synthesis stochastic process Stochastics fractal surfaces procedure random numbers stochastic modeling fractal modeling
2. BASIC MODEL OF PARTICLE SYSTEMS
A particle system is a collection of many minute particles that together represent a fuzzy object. Over a period of time, particles are generated into a system, move and change from within the system, and die from the system.
initial position => the origin of a particle system initial velocity initial color <= average RGB values and the maximum deviation from them initial transparency initial size shape => a region of newly born random particles about its origin lifetime
A particle's initial color, transparency and size are determined by mean values like MeasSpeed, maximum variations like VarSpeed of below:
InitialSpeed = MeanSpeed + Rand()*VarSpeed
More complicated generation shapes based on the law of nature or on chaotic attractors have been envisioned. eg. streaked spherical shapes => motion-blur particles
2.3 Particle Dynamics 2.4 Particle Extinction
when a particle's lifetime reaches zero
when the intensity of a particle, calculated from its color and transparency, drops belowa specified threshold
when a particle moves more than a given distance in a given direction from the origin of its parent particle system
2.5 Particle Rendering (1) Explosions and fire, the two fuzzy objects we have worekd with the most, are modeled well with the assumption that each particle can be displayed as a point light source. (Other fuzzy objects, such as clouds and water, are not.) (2) Since particles do not reflect but emit light, shadows are no longer a problem. 2.6 Particle Hierarchy
The initial direction of the particles' movement was constrained by the
system's ejection angle to fall within the region bounded by the
inverted cone. As particles flew upward, the gravity parameter pulled them back down to the planet's surface, giving them a parabolic motion path. The number of particles generated per frame was based on the amount of screen area covered by the particle system. Varying the mean velocity parameter caused the explosions to be of different heights. The rate at which a particle's color changed simulated the cooling of a glowing piece of some hypothetical material.
When a motion picture camera is used to film live action at 24 frames per second, the camera shutter typically remains open for 1/50 of a second. The image captured on a frame is actually an integration of approximately half the motion that occurred between successive frames. An object moving quickly appears blurred in the individual still frames.
> Ideas of modeling objects as collections of particles Evans & Sutherland @http://www.es.com Roger Wilson at Ohio State Alvy Ray Smith and Jim Blinn, Cosmos series Alan Norton Jim Blinn, light reflection functions
> Ideas of volumetric representations Norm Badler and Joe O'Rourke, solid modeling, "bubbleman"
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