cst 325 w7

This week, we learned about the challenges of rasterization based shadows, learned how to implement orthographic projection, projective texturing, and the shadow mapping algorithm.

There are 2 main approaches to rasterization based shadows: volume and image. In the volume based way, stencil shadows volumes are used to extrude polygons away from the light source and make those the shadow. In the image based approach, shadow mapping is used using pixels to utilize pixel depth from the light source. The image based approach is used currently. In the basic algorithm, the scene depth is rendered from the pov of the light  into a texture. The scene is rendered again from the eye and the pixel is calculated to be in or out of shadow using the depth texture. Then we see if the pixels world position is further from the light than the closest recorded distance for the pixel aka wesee if something is occluding the surface from the pov of the light. A problem created by this is aliasing and acne, where the shadows have blocky or patterned effects. This is solved using a bias offset so it calculates the depth to be slightly shorter.

Orthographic projection is used instead of perspective to match the direction of the light which is the same at all surface points.  The projection lines are parallel and perpendicular to the image plane, resulting in a view that is orthographic.

cst325 w6

This week, we learned about the basics of representing color. We also learned how scenes are illuminated as well as point, directional, and spot lighting. Finally, we studied Phong shading.

Color is a function of its wavelength represented by 3 colors and mixtures of those through addition or subtraction. Scenes are illuminated through direct and indirect lighting. When light interacts with a surface, it can scatter depending on the surface used.  Diffuse reflectors have rough surfaces so light scatters in many directions (not view dependent). In specular reflection, it is glossy so it mostly reflects in one direction (view dependent). In addition, there is ambient lighting where an object receives or reflects ambient light and gives no look of depth. The color of the pixel depends on emissive, ambient, diffuse, and specular light which depends on the light and material color in various combinations sometimes using the Lambert Law where the intensity of the reflected light is related to the orientation or where you are looking from.

Directional light doesn't depend on light source position or attenuate with distance. Point light depends on light source position and attenuates with distance. Spot light depends on light source position and attenuates with distance and buy angle from the center direction.

The basic shading models are Flat, Gouraud , and Phong. In flat shading, a single light is calculated per face which results in mach bands or a gradient effect. Dithering can be used to introduce noise to create more calculated faces and a better picture. Gouraud shading is shading per vertex in the vertex shader then sent to the fragment shader. It sometimes  creates triangles and boundaries when it should be smooth. Phong shading is shading per vertex or per pixel. Interpolate the normal across the surface and  calculating final lighting per pixel. Which removes the artifacts from Gouraud shading.

cst325 w5

This week, we worked on shaders, texturing, and transparency. We used texture mapping and filtering, applied images as textures to objects, understood methods and limitations of alpha blending, and applied alpha blending in WebGL.

Texturing is a process that takes a surface and modifies it at each location using an image, function or other data source. It makes 3D scenes look real.

In rendering, many buffers are used. A buffer is a part of memory that stores data per pixel like color and depth buffers.

The depth test using the Z-buffer compares the current fragment depth against the corresponding value in the depth buffer, if its less; it will be kept. Other tests are alpha, stencil, and scissor. The alpha test is used to remove colors where the opacity is not above a value. The stencil test is used to compare a fragment to another value in the buffer. The scissor test determines if a pixel is in a user defined rectangle, only keeping if it is inside.

Alpha blending uses an equation to determine if the new color overwrites the current buffer color and how much it contributes.

cst325 w4

This week, we learned about raytracing and it's similarities and differences from rasterization. We also learned about the CPU and GPUs role in rasterization. After, we learned about applying matrix transforms to geometry. Then we learned about how to manipulate render state and issue commands for 3D scenes in WebGL.

Polygon meshes are a collection of vertices, edges and faces that make an object. Triangles are combined with shared edges to make the object. The vertices are position, color, and texture coordinates. These meshes are used in the Rasterization pipeline because they are all triangles, are easy to calculate, and work well with hardware like CPUs and GPUs (heterogeneous computing)

The graphics pipeline is the model that describes the steps the system takes to make a 3D scene into a 2D one: Application, Geometry, Rasterization, and then to Screen. In Raytracing, the nesting order goes from pixel to object, and in Rasterization it is the opposite.

In the CPU, the application creates/loads geometry, then gives commands to the API what when and how to draw, it loads the triangle mesh data then issues a command to render. In the GPU, geometric transformations are applied to vertices and make primitives from them. Vertices are transformed from their locally defined space to the screen space, then they are assembled into triangles which receive values interpolated from the vertices. Then in Rasterization, the triangles are converted to pixels and then shaded; creating the final image. Each fragment finds the closest to the camera through the Z-value.

cst 325 w3

This week, we learned how vectors and matrices are connected. We also learned how matrices are used to manipulate space and how to solve problems with matrix operations. We also created and combined matrix transformations.

Unfortunately, I did not have very much time to work on the lab because I went out of town and only had my laptop which is horrible. In the future, I think I’ll only go out of town on holidays and everyone else is going to have to deal with the fact that I have school, which is a priority and doing construction work all weekend on a condo I have no equity in is not really my priority.

A matrix describes the relationship between 2 coordinate spaces. It is a rectangular grid of numbers arranged into rows and columns defined in rows first then columns. A matrix may have 1 row or 1 column and are called row vectors and column vectors. A transposed matrix is where the column and rows are flipped. A diagonal matrix is equal to its transpose matrix. A scalar is a regular number and you just multiply the scalar by every element in the matrix. When you multiply two matrices, the columns in A must be the same amount of rows in B, if not it is not defined.

Rotation is about a point in 2D or about the origin based on the angle value. Scale is used to make matrices larger or smaller b a factor of k. There is uniform and nonuniform scale. In uniform scale, it dilates about the origin and preserves angles and proportions, the lengths change by k units, areas change by k squared, and volumes by k cubed. Nonuniform scale has different scale factors. The absolute value of k is shorter when less than 0. When k is 0, it has orthographic projection. Is reflected when k is negative and scales (?) when k is positive. It scales along the x axis when applied about the perpendicular axis. The basis vectors are independently affected by scale vectors so one can make a big y and small x object. In reflection, it is flipped about a line 2D or plane 3D. Shear is a transformation that skews the coordinate space, stretching nonuniformly. The angles are not preserved, but the areas and volumes are preserved.

CST 325 W2

This week, we learned about raytracing. We wrote the code for the basic raytracer and used diffuse shading using the Lambert term. We then created shadows from light occlusion and used vector operations for image generation.

Raytracing uses a camera, image, object, view ray, and shadow ray. We trace the ray from the camera through each image block resulting in the following. The ray will hit the sphere, the plane, both, or none. When the ray hits the sphere and plane, only the closest is used. If an object is between the ray and the light, light is occluded and the object casts a shadow. Lambert's Law states that the intensity of the reflected light is related to it's orientation. The greater the angle of the cosine between the light ray and surface, the less intense light. If the cosine of the angle is 1, the surface is facing the light and is fully lit, if its 0, it points away and is not lit. If it's between 0 and 1, it depends on the intensity but is partially lit. When the ray hits the sphere, it will cast a shadow on the plane. If d1 is the distance from the eye to the object and d2 is the distance from the eye to the light; if d1<d2, there will be a ray intersection and a shadow. If d1>d2, there will be a ray intersection but no shadow. In other words, if it can see the light, the shadow is based on the angle, if it doesn't, it will be set to black.

CST 325

This week, we learned about how vectors and scalars are connected, how vectors are used to think about space, how different equations can represent surfaces, and how to create rays with implicit surfaces.

This week, we learned about vector operations and their history. In a vector is a displacement/oriented magnitude where an origin is not needed with a magnitude: the length of a segment. The Pythagorean theorem is used to calculate the magnitude. A unit vector is a vector with a hat and magnitude 1. In vector normalization, the unit vector v with a hat, is found by dividing the vector by the magnitude.

In vector addition, the x1 and y2 are added across and is commutative. In vector subtraction, they are subtracted across in the same way but they are anti-commutative. Vector multiplication by a scalar is multiplied across. In vector multiplication, there is no multiplication symbol because that is the cross product. In scalar division, you can divide by a scalar. In the vector dot product, the dot product of a and b is the sum of a*b. The vector cross product has a specific pattern that is hard to describe in words so it's better to see a picture example.