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Computer Vision. Chapter 6 Shading. Models of received radiation. Model of received radiation. Assuming one distant light source, the intensity that surface element j receives is: n j is the surface normal (a unit vector) s is the illumination direction
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Computer Vision Chapter 6 Shading
Model of received radiation • Assuming one distant light source, the intensity that surface element j receives is: nj is the surface normal (a unit vector) s is the illumination direction nj s is the cos of the angle between nj and s (dot product) when nj and s are unit vectors
Model of received radiation • Assuming one distant light source, the intensity that surface element j receives is: nj is the surface normal (a unit vector) s is the illumination direction nj s is the cos of the angle between nj and s (dot product) when nj and s are unit vectors Why the restriction (nj o s) > 0?
Dot product • a and b are two vectors. • It is useful to be able to calculate the angle between a and b. • That’s where the dot product comes in. • The length of a vector: (unit vectors have a length=1)
Dot product Calculating the dot product: Converting the dot product to an angle:
Dot product • Calculating the dot product: • What is the value of cos 90 degrees? • What 2 systems are used to represent angles? • Degrees and …? • What representation is used in Java? C/C++? Calculator?
Extending our model • Let’s extend our model to include the viewpoint. • Type of surfaces/surface reflection: • Diffuse (AKA Lambertian) – relatively viewpoint independent • Specular – very viewpoint dependent
Diffuse reflection AKA Lambertian (after Johann Heinrich Lambert (August 26, 1728 – September 25, 1777), a Swiss mathematician, physicist, and astronomer.)
Diffuse reflection • independent of viewpoint, V • Light reaching a surface element is reflected evenly in all directions of the hemisphere centered at that surface element.
Diffuse reflection • Albedo • amount that is diffusely reflected • Ratio (fraction) of total reflected light to total received light (by a surface element). • Low for dark surfaces (0.04 for charcoal); high for light surfaces (0.9 for fresh snow).
Diffuse reflection • Typically for “rough” surfaces.
Diffuse reflection where • j is the particular surface element, • kj is the surface albedo, • nj is the surface normal (a unit vector), and • v is the viewpoint.
Specular reflection • Mirror-like / smooth / polished surfaces. • Distributes energy in a narrow cone about the ray of reflection. • Surfaces have a “shininess” associated with them. • Values of 100 or more for shiny surfaces.
Specular reflection • Defn. specular reflection = mirror-like reflection. • Wavelength of reflected light is similar to the source and is independent of surface color.
Specular reflection • Defn., highlight = bright spot caused by the specular reflection of a light source. • Indicates that the object is wavy, metallic, or glassy.
Specular reflection where R is the reflected ray, and V is the viewpoint
Specular reflection where R is the reflected ray V is the viewpoint
Specular reflection where R is the reflected ray V is the viewpoint N is the surface normal S is the ray of received illumination (See http://mathworld.wolfram.com/Reflection.html for derivation of vector R.)
Specular vs. diffuse Specular • Wavelength of reflected light is similar to the source and is independent of surface color. • Viewpoint dependent.
Darkening with distance • The intensity of light energy reaching a surface decreases with the distance of that surface from the light source. • Mercury receives more light from the sun than the earth.
Complications • Surface models of real objects typically have both specular and diffuse components. • An apple has both specular and diffuse reflective components.
Complications • There are typically many light sources and many inter-surface reflections (referred to as ambient light).
Phong shading model Three components: • ambient • diffuse • specular
Phong shading model • For each light source (there may be many), m: • the components im,s and im,d, are the intensities (often as RGB values) of the specular and diffuse components of the light sources, respectively.
Phong shading model • A single ia term controls the ambient lighting. • It is sometimes computed as a sum of contributions from the light sources.
Phong shading model For each light source, m, • Lm is the direction vector from the point on the surface toward each light source, • N is the normal at this point of the surface, • Rm is the direction that a perfectly reflected ray of light (represented as a vector) would take from this point of the surface, and • V is the direction towards the viewer.
Phong shading model Then the shade value for each surface point Ip is calculated using this equation, which is the Phong reflection model: ka: ambient reflection constant, the ratio of reflection of the ambient term present in all points in the scene rendered
Phong shading model kd: diffuse reflection constant, the ratio of reflection of the diffuse term of incoming light (Lambertian reflectance)
Phong shading model ks: specular reflection constant, the ratio of reflection of the specular term of incoming light : is a shininess constant for this material, which decides how "evenly" light is reflected from a shiny spot, and is very large for most surfaces, on the order of 50, getting larger the more mirror-like they are.
Phong shading model • One last feature of the Phong shading model (for smooth shading): • Vectors are assigned at each polygonal vertex, and shading is interpolated across the surface of the polygon.
Summary • Shading is complicated! • We can model surfaces of objects as (coplanar) polygonal patches. • Normal vector is very important. • Each has its own color, specular, and diffuse (Lambertian) characteristics. • We can have multiple light sources in a scene. • Each may have its own: intensity, location, color, and direction. • The Phong model includes 3 components: specular, diffuse, and ambient.
