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Photo-realistic Rendering and Global Illumination in Computer Graphics Spring 2012 Visual Appearance K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology Introduction Physics-based lighting simulation Photograph The production of realistic synthetic images was and is still considered as one of the ultimate goal to reach in computer graphics. By ‘realistic’, we mean here images perceptually indistinguishable from the real scene. Direct lighting only (http://www.mpi-sb.mpg.de/resources/atrium/) 2 Introduction Illumination Light rays coming from the rest of the scene strike a surface element, and head out in different directions. We want to calculate the intensity and chromaticity values of the light that goes in the direction of the viewer from that surface element (if the viewer moves, those values will change). This is defined as the “illumination” of that surface element. 3 Introduction Global Illumination Simulates what happens when other objects affect light reaching a surface element. It is expensive to compute: the light reaching surface element may be affected by many other objects in the scene. Direct illumination: most light striking a surface element comes directly from emissive light sources in the scene. Indirect illumination: light bounces off other objects toward our surface element. When that light reaches our surface element, it brightens it. object eye direct illumination light indirect illumination object object light 4 Introduction Non-global Illumination We only concentrate on light from light sources. Ignore effects of all other objects in the scene when considering a particular surface element. A scene can be rendered much faster. But we pay a price in lost realism. We lose effects of global illumination: shadows, interobject reflection, refraction, i.e. bending of light at translucent surfaces, etc. global illumination non-global illumination 5 Introduction Interaction between light and surfaces Geometric relationship of surface with respect to lights Light incident on surface (color and intensity of emitters and reflectors in the scene) Geometric relationship of surface with respect to viewer and other (potentially blocking) objects Physical properties of the surface (material) how much light it absorbs, reflects, or refracts Approximation with no firm grounding in theory but good in practice. 6 Introduction Illumination Models describe inputs, assumptions, and outputs used to calculate illumination of surface elements. Physics-based models Require accurate input data and make few assumptions rarely have enough information to specify all those inputs. It takes a long time to compute illumination. Non-physics-based models a model that looks good enough for our application and can be calculated efficiently with available resources. 7 Illumination Models Self-luminous Object Ambient light Diffuse Reflection Atmospheric Attenuation Specular Reflection Multiple Light Sources 8 Illumination Models Self-luminous Object No external light source: non realistic Illumination Model Illumination equation I = k]. I: the resulting intensity k: object intrinsic intensity No dependence on the position of the point being shaded. Compute once for each object. 9 Illumination Models Characteristics of Surfaces ambient component to account for non-specific global light diffuse component specular component 10 Illumination Models Ambient Light Consider a diffuse/non-directional source of light. Illumination equation I = Iaka. I: intensity of the ambient light, assumed to be constant for all objects. ka: the ambient-reflection coefficient, which determines the amount of ambient light reflected from an object’s surface. The ambient-reflection coefficient: an empirical convenience. No relation to any physical property of real materials. It is used to account for all the complex ways in which light can reach an object that are not otherwise addressed by the illumination equation. 11 Illumination Models Diffuse Reflection Consider illuminating an object by a point light source whose rays emanate uniformly in all directions from a single point. The object’s brightness varies from one part to another, depending on the direction of and distance to the light source. Lambertian reflection (diffuse reflection): dull, matte surfaces The brightness depends only on the angle between the direction to the light source and the surface normal. Reflect light with equal intensity in all directions. 12 Illumination Models Diffuse Reflection Diffuse illumination equation I = Ipkdcosθ or I = Ipkd(N·L).: N and L vectors have been normalized. Directional light source If a point light source is sufficiently distant from the objects being shaded, it makes essentially the same angle with all surfaces sharing the same surface normal. L is a constant for the light source. 13 Illumination Models More realistic illumination equation so far. I = Iaka +Ipkd(N·L). 14 Illumination Models Diffuse Reflection Light-source attenuation Light energy attenuates as the distance to the light source increases. Consider such an attenuation effect in the illumination model. For a square law attenuation f att 1 2 dL f att For a richer range of effects 1 max , 1 c1 c2 d L c3d 2 L 15 Illumination Models Illumination equation so far. I = Iaka +fattIpkd(N·L). 16 Illumination Models Colored Lights and Surfaces Commonly treated by writing separate equations for each component of the color model. For RGB color system, use the triple (OdR, OdG, OdB) which defines an object’s diffuse red, green and blue components in the RGB color system. The illuminating light’s three primary components, IpR, IpG, and IpB are reflected in proportion to kdOdR, kdOdG and kdOdB. 17 Illumination Models Illumination equation so far. Iλ = Iaλ kaOdλ +fattIpλ kdOdλ (N·L). 18 Illumination Models Atmospheric Attenuation Use Depth cueing to simulate the atmospheric attenuation. More distant objects are rendered with lower intensity than are closer ones. Also consider to approximate the shift in colors caused by the intervening atmosphere. I ' s0 I (1 s0 ) I dc s0 sb ( z0 zb )(s f sb ) z f zb The goal is to modify a computed Iλ to yield the depth-cued value I’λ that is displayed. 19 Illumination Models Specular Reflection It can be observed on any shiny surface. Ex. Illuminate an apple with a bright white light. The highlight is caused by specular reflection. At the highlight, the apple appears to be not red, but white, the color of the incident light. When α is zero, the viewer can see specularly reflected light. 20 Illumination Models Specular Reflection The Phong illumination model It assumes that maximum specular reflectance occurs when α is zero and falls off sharply as α increases. The rapid fall-off is approximated by cosn α , n: the material’s specular-reflection exponent. 21 Illumination Models Specular Reflection The Phong illumination model It accounts for viewers and lights at arbitrary positions. The amount of incident light specularly reflected depends on the angle of incidence θ. I I a kaOd f att I p kd Od cos W ( ) cosn W(θ) is the fraction of specularly reflected light, which is typically set to a constant ks, the material’s specular-reflection coefficient. The color of the specular component in Phong’s illumination model is not dependent on any material property. Specular reflection is affected by the properties of the surface itself. 22 Illumination Models Specular Reflection The Phong illumination model In general specular reflection may have a different color than diffuse reflection when the surface is a composite of several materials. I I a kaOd f att I p kd Od ( N L) ksOs (R V )n Osλ is the object’s specular color. 23 Illumination Models Specular Reflection The Phong illumination model Calculating the reflection vector R=2N(N ·L)-L R·V = (2N(N ·L)-L) ·V) The halfway vector Alternative formulation of Phong’s model uses the half way vector H, which is defined as H = (L+V)/|L+V|. It is known as the direction of maximum highlights. If the surface is oriented so that its normal were in the same direction as H, the viewer sees the brightest specular highlight. 24 Illumination Models Improving the Point-Light-Source Model Real light sources do not radiate equally in all directions. In Phong’s model, a point light source has only an intensity and a position. Warn’s method: Easily implemented lighting controls That can be added to any illumination equation. To model some of the directionality of the lights. A light L is modeled by a point on a hypothetical specular reflecting surface. The surface is illuminated by a point light source L’ in the direction L’. 25 Illumination Models Improving the Point-Light-Source Model Warn’s method A light L is modeled by a point on a hypothetical specular reflecting surface. The surface is illuminated by a point light source L’ in the direction L’. Then use the Phong illumination equation to determine the intensity of L at a point on the object in terms of the angle γ between L and L’. 26 Illumination Models Improving the Point-Light-Source Model Warn’s method Assume that the reflector reflects only specular light and has a specular coefficient of 1, then the light’s intensity at a point on the object is: IL’λ cosp γ or IL’λ (-L ·L’)p 27 Illumination Models Improving the Point-Light-Source Model To restrict light’s effects to a limited area of the scene, Warn implemented flaps and cones. Flaps confine the effects of the light to a designated range in x, y, and z world coordinates. We can create a sharply delineated spotlight through the use of a cone whose apex is at the light source and whose axis lies along L’. 28 Illumination Models Multiple Light Sources If there are m light sources, then the terms for each light source are summed. I I a kaOd The f 1i m att i I p i kd Od ( N Li ) ks Os ( Ri V ) n summation harbors a new possibility for error. Iλ can now exceed the maximum displayable pixel value. Clamp each Iλ individually. Considers all of a pixel’s Iλ values together. If at least one is too big, each is divided by the largest to maintain the hue and saturation at the expense of the value. 29 Shading Models for Polygons We can shade any surface by calculating the surface normal at each visible point and applying the desired illumination model at that point. This brute-force shading model is expensive!!! Efficient Shading Methods Constant shading Interpolated shading Polygon mesh shading Gouraud Shading Phong Shading 30 Constant Shading Determine a single intensity value and use it to shade an entire polygon. Sample the value of the illumination equation once for each polygon and hold the value across the polygon to reconstruct the polygon’s shade. This approach is valid if The light source is at infinity, so N ·L is constant across the polygon face. The viewer is at infinity, so N ·V is constant across the polygon face. The polygon represents the actual surface being modeled and is not an approximation to a curved surface. 31 Interpolated Shading Shading information is linearly interpolated across a triangle from values determined for its vertices. Gouraud generalized this technique to arbitrary polygons. 32 Polygon Mesh Shading Objective: how to render a polygon mesh so that it looks as much as possible like a curved surface. If each polygonal facet is shaded individually, then a faceted appearance is generated. True for constant shading, interpolated shading or even per-pixel illumination calculations Two adjacent polygons of different orientation have different intensities along their borders. 33 Polygon Mesh Shading Simple solution of using a finer mesh turns out to be surprisingly ineffective. The perceived difference in shading between adjacent facets is accentuated by the Mach band effect. The Mach band effect exaggerates the intensity change at any edge where there is a discontinuity in magnitude or slope of intensity. At the border between two facets, the dark facet looks darker and the light facet looks lighter. 34 Polygon Mesh Shading The Mach Band Effect At the border between two facets, the dark facet looks darker and the light facet looks lighter. It is caused by lateral inhibition of the receptors in the eye. The more light a receptor receives, the more that receptor inhibits the response of the receptors adjacent to it. 35 Polygon Mesh Shading Gouraud Shading: intensity interpolation shading or color interpolation shading. It eliminates intensity discontinuities. But the bright ridges on objects such as the torus and cone are Mach bands caused by a rapid, although not discontinuous, change in the slope of the intensity curve. Gouraud shading does not completely eliminate such intensity changes. 36 Polygon Mesh Shading Gouraud Shading Steps Compute the normal at each vertex. Find vertex intensities by using the vertex normal vectors with a desired illumination model. Each polygon is shaded by linear interpolation of vertex intensities along each edge and then between edges along each scan line. 37 Polygon Mesh Shading Phong Shading It is known as normal-vector interpolation shading. It interpolates the surface normal vector N, rather than the intensity. Interpolation occurs across a polygon span on a scan line, between starting and ending normals for the span. These normals are themselves interpolated along polygon edges from vertex normals that are computed. 38 Polygon Mesh Shading Gouraud Shading vs. Phong Shading Phong shading yields substantial improvements over Gouraud shading when an illumination equation with a specular-reflectance term is used since highlights are reproduced more faithfully. 39 Polygon Mesh Shading Gouraud Shading vs. Phong Shading Phong shading yields substantial improvements over Gouraud shading when an illumination equation with a specular-reflectance term is used since highlights are reproduced more faithfully. Reduces Mach-band problems in most cases. Gouraud Shading Phong Shading 40 Comparison 41 Polygon Mesh Shading Problems with Interpolated Shading Polygonal silhouette No matter how good an approximation an interpolated shading model offers to the actual shading of a curve surface, the silhouette edge of the mesh is still clearly polygonal. Curved surface models need to be considered. Perspective distortion Anomalies are introduced because interpolation is performed after perspective transformation in the 3D screen-coordinate system, rather than in the WC system. Orientation dependence 42 Polygon Mesh Shading A Problems with Interpolated Shading Problems at shared vertices Shading discontinuity. Unrepresentative vertex normals C B Computed vertex normals may not adequately represent the surface’s geometry. -> More subdivision of the polygons is necessary. 43 Surface Detail (Simulation of missing surface detail) Surface-Detail Polygons Add gross detail through the use of surface-detail polygons to show features on a base polygon. Each surface-detail polygon is coplanar with its base polygon. It does not need to be compared with other polygons during visible-surface determination. 44