Illumination Models and Shading

Transcription

1 1 Illumination Models and Shading Motivation: In order to produce realistic images, we must simulate the appearance of surfaces under various lighting conditions. Illumination Models: Given the illumination incident at a point on a surface, what is reflected? 1

2 3 Illumination Model Parameters 4 From Illumination Models to Rendering Lighting effects are described with models that consider the interaction of light sources with object surfaces. The factors determining the lighting effects are: The light source parameters: Positions. Electromagnetic Spectrum. Shape. The surface parameters Position. Reflectance properties. Position of near b surfaces. The ee (camera) parameters Position. Sensor spectrum sensitivities. Illumination models is used to calculate the intensit of light that is reflected at a given point on a surface. Rendering methods use the intensit calculations from the illumination model to determine the light intensit at all piels in the image. Considers light propagation between surfaces in the scene.

3 5 Light Source Models A B Point Source (A): All light ras originate at a point and radiall diverging. A reasonable approimation for sources whose dimensions are small compared to the object size. Parallel source (B): Light ras are all parallel. Ma be modeled as a point source at infinit (the sun). Distributed source (C): All light ras originate at a finite area in space. A nearb sources such as fluorescent light. C 6 Illumination Models Simplified and fast methods for calculating surfaces intensities. Calculations are based on optical properties of surfaces and the lighting conditions (no reflected sources nor shadows). Light sources are considered to be point sources. A reasonabl good approimation for most scenes. 3

4 7 Ambient Light Assume there is some non-directional light in the environment (background light). The amount of ambient light incident on each object is a constant for all surfaces and over all directions. The reflected intensit I amb of an point on the surface is: 8 Eamples: Ambient light reflections I amb =K a I a I a - the ambient light intensit. K a [0,1] - the surface ambient reflectivit. In principle I a and K a are functions of color, so we have I R amb, I G amb, I B amb 4

5 9 Diffuse Reflection 10 A B Diffuse (Lambertian) surfaces are rough or grain (like cla, soil, fabric). The surface appears equall bright from all viewing directions. This is because a surface (A) perpendicular to the light direction is more illuminated than a surface (B) at an oblique angle. The reflected intensit I diff of an point on the surface is: The brightness at each point is proportional to cos(θ): N θ L I diff =K d I p cos(θ)=k d I p (N L) I p - the point light intensit. Ma appear as attenuated source f att (r)i P K d [0,1] - the surface diffuse reflectivit. N - the surface normal. L - the light direction. 5

6 11 Diffuse reflections from different light directions 1 Ambient surface Diffuse surface 6

7 13 14 Commonl, there are two tpes of light sources: A background ambient light. A point light source. The updated illumination equation is this case is: K d I=I diff +I amb =K d I p N L + K a I a 0.5 Note this is the model for one color and it should be duplicated for each channel: I R, I G, I B. 1.0 K a 7

8 15 Specular Reflection Shin and gloss surfaces (like metal, plastic) with highlights. Reflectance intensit changes with reflected angle. For an ideal specular surface (mirror) the light is reflected in onl one direction - R. However, most objects are not ideal mirrors (gloss objects) and the reflect in the immediate vicinit of R. L θ N θ R L θ N θ R φ V 16 The Phong Model: Reflected specular intensit falls off as some power of cos (φ): I spec =K s I p cos n (φ)=k s I p (R V) n K s - the surface specular reflectivit. n - specular-reflection parameter, determining the deviation from ideal specular surface (for mirror n= ). N N L R L R φ φ V V Shin surface Large n Dull surface Small n Ideal specular surface non-ideal specular surface 8

9 Plots of cos n (φ) for several specular parameter n. 1 The updated illumination equation combined with diffuse reflection is: I= I amb +I diff +I spec = K a I a + I p (K d N L+K s (R V) n ) If several light sources are placed in the scene: I= I amb +Σ k (I k diff+i k spec) n=1 n=8 n=64 9

10 19 0 Several reflections with different specular parameters K s 0. n= n= n=3 K d 10

11 1 Polgon Rendering Methods Diffuse surface Given a freeform surface, one usuall approimates the surface as a polhedra. How do we calculate in practice the illumination at each point on the surface? Appling the illumination model at each surface point is computationall epensive. With additional specular component 11

12 3 Flat Shading 4 Gouraud Shading A single intensit is calculated for each surface polgon. A fast and simple method. Gives reasonable result onl if all of the following assumptions are valid: The object is reall a polhedron. Light source is far awa from the surface so that N L is constant over each polgon. Viewing position is far awa from the surface so that V R is constant over each polgon. Renders the polgon surface b linearl interpolating intensit values across the surface. The algorithm: 1. Determine the average unit normal at each polgon verte.. Appl an illumination model to each verte to calculate the verte intensit. 3. Linearl interpolate the verte intensities over the surface polgon. 1

13 13 5 = k k k k V N N N Step no 1 The normal N v of a verte is an average of all neighboring normals: 6 I 1 I I 3 I 4 I 5 scan line Step no I I I + = I I I + = I P p p 5 p I I I + =

14 7 8 Gouraud Shading of a sphere Phong Shading A more accurate method is for rendering a polgon surface is to interpolate normal vectors, and then appl the illumination model to each surface point. The algorithm: 1. Determine the average unit normal at each polgon verte.. Linearl interpolate the verte normals over the surface polgon. 3. Appl the illumination model along each scan line to calculate piel intensities for each surface point. 14

15 9 30 Phong Shading of a sphere Flat Gouraud Phong 15

16 31 Flat Shading Gouraud Shading Phong Shading 16