# Ppt on surface area and volume of frustum

##### Fast and Accurate Soft Shadows using a Real-Time Beam Tracer Ravi Ramamoorthi Columbia Vision and Graphics Center Columbia University

triangle.  Hit beams must continue KD tree traversal until its hit distance is fully contained by one of the beam’s tmin planes and all of its tmax planes. Outline  Motivation  Beam Tracing Algorithm  Beam-Triangle Intersection  Beam-KD-tree/ volumes [Laine et al. 2005, Lehtinen et al. 2006] Comparison Setup  Use our optimized ray tracer for comparison  Not clear how to adapt frustum methods/ray packets  512x512 resolution (linear scaling with res)  Our kd-tree builder (basic surface area heuristic/

##### GCSE Mathematics Route Map – Higher Tier Assessment Order Unit 2 – March Year 10 Unit 1 – June Year 10 Unit 3 – June Year 11 Notes –  A lot of Unit 2.

shapes  work out the area of complex shapes made from a combination of known shapes  work out the area of segments of circles  work out volumes of frustums of cones  work out volumes of frustums of pyramids  calculate the surface area of compound solids constructed from cubes, cuboids, cones, pyramids, cylinders, spheres and hemispheres  solve real life problems using known solid shapes Unit 3 – Perimeter, Area and VolumeUnit 3 – Perimeter, Area and Volume (Slide 3 of 3) View previous page Unit/

##### GCSE Mathematics Route Map – Higher Tier Teaching Order Unit 2 – Year 10 Unit 1 – Year 10 Unit 3 – Year 11 Notes – A lot of Unit 2 time has been given.

shapes  work out the area of complex shapes made from a combination of known shapes  work out the area of segments of circles  work out volumes of frustums of cones  work out volumes of frustums of pyramids  calculate the surface area of compound solids constructed from cubes, cuboids, cones, pyramids, cylinders, spheres and hemispheres  solve real life problems using known solid shapes Unit 3 – Perimeter, Area and VolumeUnit 3 – Perimeter, Area and Volume (Slide 3 of 3) View previous page Unit/

##### 1 SSD99 Tutorial Multiresolution in Terrain Modeling Leila De Floriani, Enrico Puppo University of Genova Genova (Italy)

volume, curvature, surface normal, etc... 46 SSD99 Tutorial Triangle quality measures o A TIN should have triangles as much compact as possible o Elongated triangles (slivers) cause numerical errors and unpleasant visual effects o Compactness of a triangle [Gueziec, 1995]: where A is the area and/with: maccuracy decreasing linearly with distance from the viewpoint mregion of interest coincident with the view frustum 159 SSD99 Tutorial...VARIANT......Multiresolution visualization... Uniform resolution: 12701 /

##### The “Dark” Side of Game Development

channels… Use XNA RenderTarget2D Writeable surface, can convert to texture Easy to use Creating the Shadow Map Matrices Need light’s view, projection matrices Choice in projection Ortho best for large, directional lights (i.e. sun) LightProj = Matrix.CreateOrthographic(w, h, n, f) w, h are width and height of view volume n, f are near and far planes of the view volume Recommend calculating these instead/

##### Exploiting Temporal Coherence in Ray Casted Walkthrougs Vlastimil Havran, Jiří Bittner and Hans-Peter Seidel AG4, MPI Informatik, Saarbruecken, Germany.

al., 00: Frame Coherent Volume Rendering. New Algorithm: Overview Main Idea: - Compute a single intersection of the ray with an object, if possible - If not possible -> ordinary ray shooting algorithm First frame: use ordinary ray shooting, remember intersection points in 3D space Next frames: reproject points, check if we can decide on intersection objects Properties: intersection points and surface normals compute correctly (unlike in/

##### CS 4731: Computer Graphics Lecture 18: Hidden Surface Removal Emmanuel Agu.

surface in scene To save time, draw only surfaces we see Surfaces we cannot see and their elimination methods: Occluded surfaces: hidden surface removal (visibility) Back faces: back face culling Faces outside view volume/each polygon { for each pixel (x,y) inside the polygon projection area { if (z_polygon_pixel(x,y) > depth_buffer(x,y) ) { /Frustum Culling Remove objects that are outside the viewing frustum Done by 3D clipping algorithm (e.g. Liang-Barsky) Ray Tracing Ray tracing is another example of/

##### MIT EECS 6.837, Durand and Cutler Real-Time Shadows.

Shadow Volumes MIT EECS 6.837, Durand and Cutler Cast Shadows on Planar Surfaces Draw the object primitives a second time, projected to the ground plane MIT EECS 6.837, Durand and Cutler Limitations of /volumes 2. Clip the shadow volumes to the view frustum 3. "Z-Fail" shadow volumes 0 MIT EECS 6.837, Durand and Cutler 1. Test Eye with Respect to Volumes Adjust initial counter value Expensive 0 +1 0 MIT EECS 6.837, Durand and Cutler 2. Clip the Shadow Volumes Clip the shadow volumes to the view frustum and/

##### Transformations Angel: Chapter 3 ppt from Angel, AW, Harvard and MIT Open Courseware, etc. CSCI 6360/4360 v=T(u)

frame – eye at origin Allows use of canonical viewing procedures Type of projection (parallel or perspective) and part of world to image (clipping or view volume) Normalization lets clip against simple cube regardless of projection Delay final projection until end –Important for hidden-surface removal to retain depth information as long as possible OpenGL Clip Space In OpenGL clip space, viewing frustum is mapped to a cube that/

##### 1 LODMODELSLODMODELS VIS98 Tutorial Level of Detail (LOD) Models Part One.

surfaces and volume data 3 LODMODELSLODMODELS VIS98 Tutorial LOD Models o Layered models mdescription of a sequence of few meshes each of which represents an object at a different resolution o Multiresolution models mdescription of a virtually continuous set of/set describes the region of interest of the query Examples of focus sets: mPoint : point location query mLine/polyline : segment/line interference query mRegion : window query, region interference query mVolume: view frustum VIS98 Tutorial...Spatial /

##### Engineering Mechanics: Statics Chapter 9: Center of Gravity and Centroid Chapter 9: Center of Gravity and Centroid.

the volume of the cone The theorems of Pappus and Guldinus are used to find the surfaces area and volume of any object of revolution provided the generating curves and areas do not cross the axis they are rotated 9.4 Theorems of Pappus and Guldinus Surface Area Area of a surface of revolution = product of length of the curve and distance traveled by the centroid in generating the surface area 9.4 Theorems of Pappus and Guldinus Volume Volume of a body of revolution = product of generating area and distance/

##### OpenGL A Brief Overview. What is OpenGL? It is NOT a programming language. It is a Graphics Rendering API consisting of a set of functions with a well.

) Alternative to glFrustum(..). Creates a matrix for an perspective viewing frustum and multiplies the current matrix by it. Alters the Projection matrix. Note: fovy is the field of view (fov) angle between the top and bottom planes of the clipping volume. aspect is the aspect ratio Perspective Projection Commands Enabling GL Features Features – lighting, hidden-surface removal, texture mapping, etc… Each feature will slow down the rendering/

##### MATERIALS & CONSTRUCTION TECHNOLOGY Chapter No. 1 Concrete lecture 1- concrete PALESTINE UNIVERSITY Faculty of Applied Engineering and Urban Planning Dept.

high fineness means more strength,more workability,and more interaction The exceeded fineness cause – Increases in surface area and more released reaction heat – More cost of KLinker – Increase the cement volume decrees. Fineness test. This test is done to verify the standard of grinding of cement. We know that rate of hydration and hydrolysis of cement, depend, upon its fineness and thus testing of the fineness of the cement is an essential feature. Fineness/

##### Chapter 7. Three-Dimensional Viewing Sang Il Park Sejong University Lots of slides are stolen from Jehee Lee’s.

complex to analyze easily Area Subdivision Four possible relationships between polygon surfaces and a rectangular section of the viewing plane Terminating criteria –Case 1: An area has no inside, overlapping, or surrounding surfaces (all surfaces are ourside the area) –Case 2: An area has only one inside, overlapping or surrounding surfaces –Case 3: An area has one surrounding surface that obscures all other surfaces within the area boundaries Octrees Visible-surface identification is accomplished by/

##### Conduction Conceptests

the slower the heat transfer rate. A cone frustum is conducting heat at steady state with no generation A cone frustum is conducting heat at steady state with no generation. If the frustum is insulated as shown, the heat flux in/as volume/surface area, and k is thermal conductivity. To keep the Biot number small would require either a small convective heat transfer coefficient or characteristic length or large thermal conductivity. -Effects of density on heat transfer would depend on the material and, /

##### Unit 3 Revision Notes - Higher

of the cone is h The curved surface area of the cone and the curved surface area of the hemisphere are equal (a) Show that l = 2r (2) (b) Find the perpendicular height, h, of the cone in terms of r. (2) (c) Find the ratio of the volumes of the cone and the hemisphere. (2) Be prepared to use algebra to solve problems involving volume and surface area If the curved surfaces of/volume of the whole cone including the missing top which shouldn’t really be there is 1/3 × π × 62 × 3 = 36π The volume of the frustum /

##### Geology and Surveying (Part B - Surveying) Volumes and DTMs

a Volume of a Frustum A1 h A2 A1 and A2 are parallel Perpendicular height between A1 and A2 h A2 A1 and A2 are parallel Volume of a Wedge h = Vertical Height a b d h If d=a Volume of a Prismoid A Prismoid is a solid having for its ends any two parallel plane figures, and having plane sides. l A2 A1 Trapezoidal Rule for Volumes Prismoidal Formula End Area/

##### Data Visualization And Mining Using The GPU Sudipto Guha (Univ. of Pennsylvania) Shankar Krishnan (AT&T Labs - Research) Suresh Venkatasubramanian (AT&T.

Description of all object, surface and light source geometry and transformations Lighting model: Computational description of object and light properties, interaction (reflection, scattering etc.) Synthetic viewpoint (or Camera location): Eye position and viewing frustum Raster /simulation:  Fluid flow visualization for graphics and scientific computing  One of the most well-studied and successful uses of the GPU. Image processing and analysis  A very hot area of research in the GPU world  Numerous /

##### MEL713 – DESIGN OF I.C. ENGINES: COMPONENTS & SUB-SYSTEMS P M V Subbarao Professor Mechanical Engineering Department Laboratory & Design Practicals …..

different rated conditions –Calculate engine volume, piston speed, and cylinder surface area as a function of crank angle –Draw a cylinder schematic and identify the bore, stroke, crank radius, TDC, BDC, and crank angle List of Laboratory Experiments Study of Anatomy of A Single Cylinder Diesel Engine. Study of Anatomy of A Multi-cylinder Diesel Engine. Disassembly and assembly of A single cylinder Diesel Engine. Measurement of Valve Timing of A Single Cylinder Diesel Engine. Performance/

##### UNIT- I 2D PRIMITIVES. Line and Curve Drawing Algorithms.

boundaries of a closed surface. By choosing an arbitrary interior point, the complete interior of the surface will be filled with the color of the user’s choice. Interactive Filling, cont’d Definition: An area or/volume so that the centerline of the frustum is perpendicular to the view plane 2.Scale the view volume with a scaling factor that depends on 1/z. A shear operation is to align a general perspective view volume with the projection window. The transformation involves a combination of z-axis shear and/

##### SAN DIEGO SUPERCOMPUTER CENTER University of California, San Diego Volume Graphics Technology to Tools David R. Nadeau Principal Scientist San Diego Supercomputer.

of California, San Diego Evolution of volume graphics Volume graphics today… …is where surface graphics was 15 years ago –We are at the start of a transition from technology to tool What enabled story telling and games for surface graphics? What might do the same for volume/ a small volume… History Rendering Authoring Data source: Product literature SAN DIEGO SUPERCOMPUTER CENTER University of California, San Diego What resolution can we see? Eye’s lens focuses light onto retina –Fovea = focus area = center /

##### Transformations Angel: Chapter 3 ppt from Angel, AW, Harvard and MIT Open Courseware, etc. CSCI 6360 v=T(u)

viewing procedures Type of projection (parallel or perspective) and part of world to image (clipping or view volume) Normalization lets clip against simple cube regardless of projection Delay final projection until end –Important for hidden-surface removal to retain depth information as long as possible OpenGL Clip Space Overview, model-view-projection In OpenGL clip space, viewing frustum is mapped to a cube that extends from -1/

##### 9.3 Composite Bodies Consists of a series of connected “simpler” shaped bodies, which may be rectangular, triangular or semicircular A body can be sectioned.

the volume of the cone The theorems of Pappus and Guldinus are used to find the surfaces area and volume of any object of revolution provided the generating curves and areas do not cross the axis they are rotated 9.4 Theorems of Pappus and Guldinus Surface Area Area of a surface of revolution = product of length of the curve and distance traveled by the centroid in generating the surface area 9.4 Theorems of Pappus and Guldinus Volume Volume of a body of revolution = product of generating area and distance/

##### Controlling a Virtual Camera Ross Ptacek University of Alabama Birmingham.

outer surface of the volume (T p ) Sampling  Constant interval (easy but may lose info)  Curvature Based (harder, more accurate) Intersect T p with T s to find collisions Type 2 Collisions Compute NCP at some sampling density  Similar sampling issues as before Triangulate each NCP and intersect with T s Add these triangles to T p Path correction In general, find problem areas and push/

##### 3/16/04James R. McGirr1 Interactive Rendering of Large Volume Data Sets Written By : Stefan Guthe Michael Wand Julius Gonser Wolfgang Straβer University.

using hardware texture mapping 3/16/04James R. McGirr3 Motivation Many areas in medicine, computational physics, biology, etc, deal with large volumetric data sets that demand adequate visualization. Direct Volume Rendering – Each point in space is assigned a density for the emission and absorption of light and the volume renderer computes the light reaching the eye along viewing rays. Can be done efficiently using texture mapping/

##### VPF Data Viewer Using OpenGL. About VPF Vector Product Format - MIL-STD-2407 Issued 28 June 1996 Consists of a combination of Vector data (for drawing)

sample database downloaded from NIMA contained 544 MB of raw data. The process of removing extraneous objects from being drawn is known as culling. There are many methods of culling commonly used in 3D graphics, including: View-Frustum Culling Bounding-Volume Culling Bounding-Volume Hierarchies Backface Culling Cells and Portals Levels of Detail VPF Topology Levels Method of changing the level of detail in the VPF data. Included in the/

##### Chapter 7. Three-Dimensional Viewing Sang Il Park Sejong University Lots of slides are stolen from Jehee Lee’s.

complex to analyze easily Area Subdivision Four possible relationships between polygon surfaces and a rectangular section of the viewing plane Terminating criteria –Case 1: An area has no inside, overlapping, or surrounding surfaces (all surfaces are ourside the area) –Case 2: An area has only one inside, overlapping or surrounding surfaces –Case 3: An area has one surrounding surface that obscures all other surfaces within the area boundaries Octrees Visible-surface identification is accomplished by/

##### X-STD MATHEMATICS IMPORTANT 5 MARKS PROBLEMS

= 17.5 – 3.5 = 14cm Volume of wood = volume of hemisphere + volume of cone 2 2 A cup is in the form of a hemisphere surmounted by a cylinder A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is 8 cm and the total height of the cup is 11.5 cm. Find the total surface area of the cup. Cylindrical part Height = 8/

##### OpenGL A Brief Overview. What is OpenGL?  It is NOT a programming language.  It is a Graphics Rendering API consisting of a set of function with a well.

to an identity matrix 23 Enabling GL Features Features – lighting, hidden-surface removal, texture mapping, etc… Each feature will slow down the rendering /frustum and multiplies the current matrix by it. Alters the Projection matrix. 42 Note: fovy is the field of view (fov) angle between the top and bottom planes of the clipping volume/ Defines an area of the window into which the final image is mapped (x, y) specifies the lower-left corner of the viewport (width, height) specifies the size of the viewport /

##### Session 18 – 3D shapes. Basic 3D shapes  Discussion of  Nets  Isometric projection  Faces, edges and vertices  Ex30.1 on the board.

all the way through.  Its volume is found by working out the area of the end face, and multiplying this by the length of the shape.  Ex 30.5 Q1,2 and 3 Surface area of a prism Total surface area of a prism is found by adding up the area of each face. For example, a triangular prism is made up of 2 identical triangular faces and 3 rectangular ones. Surface area of a cylinder h  Ex30.6/

##### 1 What is Computer Graphics Computer graphics is commonly understood to mean the creation, storage and manipulation of models and images. (Andries van.

planes to define max and min distance to viewer Introduction to 3D clipping 265 In 3D a clip volume needs to be defined Example for “ perspective ” 3D Introduction to 3D clipping 266 Result is a finite clip volume of space This shape is a named a frustum Introduction to 3D clipping 267 3-D Extension of 2-D Cohen-Sutherland Algorithm, Outcode of six bits. A bit/

##### Basic Math Area Formulas

= 20 ft 51032 ft2 3533 ft2 1649 ft2 Frustum of a Right Circular Cone The part of a right circular cone between the base and a plane parallel to the base whose distance from the base is less than the height of the cone. Height: h      Radius of bases: r, R      Slant height: s      Lateral surface area: S      Total surface area: T      Volume: V s = sqrt([R-r]2+h2) S/

##### Real-Time Rendering COMS 6998-3, Lecture 9. Real-Time Rendering Demo Motivation: Interactive rendering with complex natural illumination and realistic,

area light ??[Moeller02] [Blinn76] [Heidrich00] [Crow77] [Ashikhmin02] our technique Non-Interactive[Matusik02] Motivation Better light integration and transport dynamic, area lights self-shadowing interreflections For diffuse and glossy surfaces At real-time rates point light area light area lighting, no shadows area/ the eye’s point-of-view For each rasterized fragment determine fragment’s XYZ position relative to the light this light position should be setup to match the frustum used to create the depth/

##### 3D Graphics Rendering and Terrain Modeling Technology and Historical Overview By Ricardo Veguilla.

. Color is calculated for each vertex and interpolated across the polygon Phong Shading The normal vectors are interpolated across the surface of the polygon The color of each point within the polygon is calculated from its corresponding normal vector Polygon shading techniques compared Viewing frustum Segment of the 3D world to be rendered Objects outside the viewing volume are ignored. Hidden surface determination Not all objects inside the/

##### INB382/INN382 Real-Time Rendering Techniques Lecture 9: Global Illumination Ross Brown.

all the possible light paths to the surface – the more paths, the greater the level of realism Radiosity and Ray Tracing Thus global illumination is divided into two main approaches Radiosity – calculation of light as radiation transfer through volume of air Ray Tracing – calculation of light as a set of discrete ray samples through a volume We have covered the general idea of ray tracing Now we illustrate the main/

##### 1 Proper Univariate and Multivariate Integrals Rajandra Chadra Bhowmik Lecturer Dept. of Mathematics Pabna Science and Technology University.

the volume of a pyramidal frustum. The first documented systematic technique capable of determining integrals is the method of exhaustion of Eudoxus (circa 370 BC), which sought to find areas and volumes by breaking them up into an infinite number of shapes for which the area or volume was known. This method was further developed and employed by Archimedes (287 BC - 212 BC) and used to calculate areas for parabolas and an approximation to the area of a/

##### Advanced Computer Graphics Spring 2009 K. H. Ko Department of Mechatronics Gwangju Institute of Science and Technology.

surface area.  Minimizing this area increases the efficiency of any intersection algorithm as a rejection is never slower to compute than an intersection. It is often better to minimize the volume of BV for collision detection algorithms. 14 AABB and k-DOP Creation AABB  The simplest bounding volumes to create is an AABB.  Take the minimum and maximum extents of the set of/it misses. A generalized of the slabs method can be used to compute the intersection of a ray with a k-DOP, frustum, or any convex /

##### University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2010 Tamara Munzner Viewing/Projection V,

Example view volume left = -1/Of Color elements of color: 49 Basics of Color physics illumination electromagnetic spectra reflection material properties surface geometry and microgeometry polished versus matte versus brushed perception physiology and neurophysiology perceptual psychology 50 Light Sources common light sources differ in kind of/of time, per unit solid angle, and per unit projected area of the source (related to the luminance of the source) lightness/brightness: perceived intensity of/

##### Final Review 2 University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2016 Tamara Munzner.

6 Review: Projection Normalization warp perspective view volume to orthogonal view volume render all scenes with orthographic projection! aka /the field of view / frustum solved by clipping – polygon is backfacing solved by backface culling – polygon is occluded by object(s) nearer the viewpoint solved by hidden surface removal / – all positive, unit area – Y is luminance Backstory: Spectral Sensitivity Curve 80 Review: CIE Chromaticity Diagram and Gamuts plane of equal brightness showing chromaticity gamut/

until: –rectangle contains part of 1 projected surface –rectangle contains part of no surface –rectangle is size of pixel 6/14/2015©Zachary Wartell Area-Subdivision Method We need tests that can quickly determine tell if current area is part of one surface or if further subdivision is needed. Four cases for relation between surface and rectangular area: surrounding surface overlapping surface inside surface outside surface 6/14/2015©Zachary Wartell Area-Subdivision: Stopping Conditions Recursive subdivision/

##### Wilf LaLonde ©2012 Comp 4501 95.4501 Shadows. Wilf LaLonde ©2012 Comp 4501 How Do I Draw a Pixel? Shadows volumes: Used in Doom (Expensive) From lights,

of Aliasing Wilf LaLonde ©2012 Comp 4501 An Example of Acne Wilf LaLonde ©2012 Comp 4501 Reduce areas of extreme mag- and mini- fications (increase resolution or change the engine architecture) Perspective shadow maps => warp the shadow space to the view space Cascaded shadow maps => use different shadow maps in different parts of the frustum/Pixel is blocked by something... } Wilf LaLonde ©2012 Comp 4501 This is Called Surface Acne or Z-Fighting Wilf LaLonde ©2012 Comp 4501 Eliminating Acne From “Real-time /

##### Section 12.4 & 12.5  Volume of Prisms & Cylinders olume of Pyramids & Cones  Go over Quizzes.

& 12.5  Volume of Prisms & Cylinders olume of Pyramids & Cones  Go over Quizzes Volume of Prisms and Cylinders What physical process did we relate to surface area? What about volume? Formula for the Volume of a Prism and Cylinder Prism Cylinder REMEMBER: B – represents the area of one base h – represents the height of the prism or cylinder cross section Example 1: A triangular prism has a height of 10 cm. The lengths of the base edges/

##### Announcements Always the alias rather than either of us directly for anything – Better.

– Leaves represent convex polytope Some solid, some empty Some have infinite area/volume Works best for indoor environments (flat, man-made surfaces) Used by original Doom and Quake – Still used today (Source, Unreal, Call of Duty IW engine) a b c d e f g h b / 3 – Seen from portal 2 Don’t draw room 4 – Not seen from portal 3 Player View frustum 1 2 3 4 Portal pros and cons Pros – Easy collision detection and raytracing – Can be used for dynamic objects (unlike BSP trees) – Portals can point to non-adjacent/

##### Advanced Computer Graphics Spring 2014 K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology.

to their projection along the selected axis, resulting in a balanced tree.  Minimize the sum of the volumes (or surface areas) of the child volumes  Minimize the maximum volume (surface area) of the child volumes  Minimize the volume (surface area) of the intersection of the child volumes  Maximize the separation of child volumes  Divide primitives equally between the child volumes  Combinations of the previous strategies. 15 Top-down Construction Stopping criteria  The node contains just a single/

##### University of British Columbia CPSC 314 Computer Graphics May-June 2005 Tamara Munzner Sampling, Virtual Trackball,

of view / frustum solved by clipping polygon is backfacing solved by backface culling polygon is occluded by object(s) nearer the viewpoint solved by hidden surface removal for efficiency reasons, we want to avoid spending work on polygons outside field of view or backfacing for efficiency and/projection transform each vertex maintains z coordinate relative to eye point can do this with canonical viewing volumes 108 The Z-Buffer Algorithm augment color framebuffer with Z-buffer or depth buffer which stores Z/

##### University of British Columbia CPSC 414 Computer Graphics © Tamara Munzner 1 Visibility: Z Buffering Week 10, Mon 3 Nov 2003.

of view / frustum clipping –polygon is backfacing backface culling –polygon is occluded by object(s) nearer the viewpoint hidden surface removal Week 10, Mon 3 Nov 03 © Tamara Munzner8 Back-Face Culling on the surface of/ canonical viewing volumes –each vertex/ Z along edges and across spans Week/area-averaged accumulation buffer z-buffer: one visible surface per pixel A-buffer: linked list of surfaces data for each surface includesdata for each surface includes RGB, Z, area-coverage percentage,...RGB, Z, area/

##### Radiosity, Surface Detail, Textures Saravanan Manoharan EEL 5771-001 Introduction to Computer Graphics.

. It is the amount of flux from a point source contained in a small angular volume. Steradian (sr): The solid angle subtended at the center of a sphere by an area on its surface numerically equal to the square of the radius When the solid/ of energy that leaves surface i and lands on surface j Radiosity equation: Radiosity B is the energy per unit area leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy: B(x) i dA i - total energy leaving a small area/

##### The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Soft Shadows using Hardware Cameras Kyle Moore COMP 870.

get performance increase as well as quality enhancement The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL 6 My Approach Area Light Source Occluder Surface Hardware Camera View Frustum Camera’s View Average Pixels to get Occlusion percentage The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL 7 My Approach Area Light Source Occluder Surface Camera’s View The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL 8 My Application The/

##### CS248 Final Review. CS248 Final Monday, December 6, 3:30 to 6:30 pm, Gates B01 Closed book, closed notes Mainly from material in the second half of the.

Mainly from material in the second half of the quarter – will not include material from last part of last lecture (volume rendering, image-based rendering) Review session/area ALSO gets smaller as a cosine fall off! – F att x I x K d x (N L) N V I  length = cos(t) Radiance intensity: intensity/solid angle N V Lighting BRDF = Bidirectional Reflectance Distribution Function – Description of how the surface interacts with incident light and emits reflected light – Isotropic Independent of absolute incident and/

##### Demonstrative vs Plausible Reasoning Patterns of Plausible Inference Volume II By G. Polya Princeton Univ. Press 1954.

Demonstrative vs Plausible Reasoning Patterns of Plausible Inference Volume II By G. Polya Princeton Univ. Press 1954 Conjecture Any integer of the form 8N+3, where N=1,2,3,… is the sum of a square and the double of a prime N=1 then 8n+3=11 N=2 then 8n+3=19 / example The area of the lateral surface of the frustum is: Theorem:  (R+r) sq rt [(R-r) 2 + h 2 ] Can you check this result by applying to some case you already know? When R=r you get cylinder Consequence B 1 : Area is (2  R) h When r=0, and h=0 /