Visible surface detection aims to determine which parts of 3D objects are visible and which are obscured. There are two main approaches: object space methods compare objects' positions to determine visibility, while image space methods process surfaces one pixel at a time to determine visibility based on depth. Depth-buffer and A-buffer methods are common image space techniques that use depth testing to handle occlusion.
It gives the detailed information about Three Dimensional Display Methods, Three dimensional Graphics Package, Interactive Input Methods and Graphical User Interface, Input of Graphical Data, Graphical Data: Input Functions, Interactive Picture-Construction
This document discusses different types of input devices used in graphics programs. It describes six logical device classifications - locator, stroke, string, valuator, choice, and pick devices. Locator devices input coordinate positions, stroke devices record sequences of coordinates, string devices input text, valuator devices set parameter values, choice devices select menu options, and pick devices select parts of an image. Examples of physical devices that can be used for each logical device type are provided. Approaches for uniquely identifying picked objects include distance calculations and highlighting potentially selected objects.
a spline is a flexible strip used to produce a smooth curve through a designated set of points.
Polynomial sections are fitted so that the curve passes through each control point, Resulting curve is said to interpolate the set of control points.
This document contains information about 3D display methods in computer graphics presented by a group of 5 students. It discusses parallel projection, perspective projection, depth cueing, visible line identification, and surface rendering techniques. The goal is to generate realistic 3D images and correctly display depth relationships between objects.
Cubic curves are commonly used in graphics because curves of lower order commonly have too little flexibility, while curves of higher order are usually considered unnecessarily complex and make it easy to introduce undesired wiggles.
The document discusses 2D viewing and clipping techniques in computer graphics. It describes how clipping is used to select only a portion of an image to display by defining a clipping region. It also discusses 2D viewing transformations which involve operations like translation, rotation and scaling to map coordinates from a world coordinate system to a device coordinate system. It specifically describes the Cohen-Sutherland line clipping algorithm which uses region codes to quickly determine if lines are completely inside, outside or intersect the clipping region to optimize the clipping calculation.
It gives the detailed information about Three Dimensional Display Methods, Three dimensional Graphics Package, Interactive Input Methods and Graphical User Interface, Input of Graphical Data, Graphical Data: Input Functions, Interactive Picture-Construction
This document discusses different types of input devices used in graphics programs. It describes six logical device classifications - locator, stroke, string, valuator, choice, and pick devices. Locator devices input coordinate positions, stroke devices record sequences of coordinates, string devices input text, valuator devices set parameter values, choice devices select menu options, and pick devices select parts of an image. Examples of physical devices that can be used for each logical device type are provided. Approaches for uniquely identifying picked objects include distance calculations and highlighting potentially selected objects.
a spline is a flexible strip used to produce a smooth curve through a designated set of points.
Polynomial sections are fitted so that the curve passes through each control point, Resulting curve is said to interpolate the set of control points.
This document contains information about 3D display methods in computer graphics presented by a group of 5 students. It discusses parallel projection, perspective projection, depth cueing, visible line identification, and surface rendering techniques. The goal is to generate realistic 3D images and correctly display depth relationships between objects.
Cubic curves are commonly used in graphics because curves of lower order commonly have too little flexibility, while curves of higher order are usually considered unnecessarily complex and make it easy to introduce undesired wiggles.
The document discusses 2D viewing and clipping techniques in computer graphics. It describes how clipping is used to select only a portion of an image to display by defining a clipping region. It also discusses 2D viewing transformations which involve operations like translation, rotation and scaling to map coordinates from a world coordinate system to a device coordinate system. It specifically describes the Cohen-Sutherland line clipping algorithm which uses region codes to quickly determine if lines are completely inside, outside or intersect the clipping region to optimize the clipping calculation.
This document discusses various 3D transformations including translation, rotation, scaling, reflection, and shearing. It provides the transformation matrices for each type of 3D transformation. It also discusses combining multiple transformations through composite transformations by multiplying the matrices in sequence from right to left.
The document discusses the 2D viewing pipeline. It describes how a 3D world coordinate scene is constructed and then transformed through a series of steps to 2D device coordinates that can be displayed. These steps include converting to viewing coordinates using a window-to-viewport transformation, then mapping to normalized and finally device coordinates. It also covers techniques for clipping objects and lines that fall outside the viewing window including Cohen-Sutherland line clipping and Sutherland-Hodgeman polygon clipping.
Window to viewport transformation&matrix representation of homogeneous co...Mani Kanth
The document discusses window to viewport transformation and the use of homogeneous coordinates. A window defines the area of data to display, while a viewport defines where on the display device the window will appear. Window to viewport transformation maps the window coordinates to viewport coordinates using translation and resizing. Homogeneous coordinates represent points using an extra dimension, allowing rotation, scaling and other transformations to be represented using matrix multiplication.
with today's advanced technology like photoshop, paint etc. we need to understand some basic concepts like how they are cropping the image , tilt the image etc.
In our presentation you will find basic introduction of 2D transformation.
In a raster scan system, the electron beam scans across rows of the screen from top to bottom, turning intensity on and off to illuminate spots and form an image. The image definition is stored in a refresh buffer memory that holds intensity values for screen points. In a random scan system, an application and graphics package are stored in memory, and graphics commands are translated into a display file that a display processor accesses to refresh the screen. Graphics patterns are drawn by directing the electron beam along picture lines one at a time, positioning it between coordinate-defined endpoints to fill each line.
The document discusses different methods for 3D display and projection. It describes parallel projection, where lines of sight are parallel, and perspective projection, where lines converge at vanishing points. The key types of projection are outlined as parallel (orthographic and oblique) and perspective. Orthographic projection uses perpendicular lines, while oblique projection uses arbitrary angles. Perspective projection creates realistic size variation with distance and can have one, two, or three vanishing points.
The document discusses window to viewport transformation. It defines a window as a world coordinate area selected for display and a viewport as a rectangular region of the screen selected for displaying objects. Window to viewport mapping requires transforming coordinates from the window to the viewport. This involves translation, scaling and another translation. Steps include translating the window to the origin, resizing it based on the viewport size, and translating it to the viewport position. An example transforms a sample window to a viewport through these three steps.
This document discusses methods for identifying and removing hidden surfaces when rendering 3D scenes to create a realistic 2D image. It describes two approaches: object-space methods that compare whole objects, and image-space methods that decide visibility point-by-point. It focuses on the depth buffer/z-buffer method, which processes surfaces one point at a time, comparing depth values to determine visibility and store the color of visible points. It also discusses using scan line coherence to solve hidden surfaces one scan line at a time from top to bottom.
The document discusses several methods for visible surface detection or hidden surface removal in 3D computer graphics, including object space and image space methods. Object space methods determine visibility in 3D coordinates and include depth sorting and binary space partitioning (BSP) trees, while image space methods determine visibility on a per-pixel basis and include the depth-buffer or z-buffer method and ray casting. The depth-buffer method uses two buffers, a frame buffer and depth buffer, to render surfaces from back to front on a pixel-by-pixel basis. BSP trees recursively subdivide space with splitting planes to give a rendering order that correctly draws objects from back to front.
This document summarizes the scan-line rendering algorithm. It maintains two tables - an edge table containing line coordinates and surface pointers, and a polygon table containing surface properties. For each scan line, all intersecting surfaces are examined to determine the visible surface. Depths are calculated to set surface flags and populate the image buffer with intensity values from the visible surface. Coherence between scan lines is exploited to reuse prior visibility calculations where edge intersections remain the same.
The document describes different algorithms for filling polygon and area shapes, including scanline fill, boundary fill, and flood fill algorithms. The scanline fill algorithm works by determining intersections of boundaries with scanlines and filling color between intersections. Boundary fill works by starting from an interior point and recursively "painting" neighboring points until the boundary is reached. Flood fill replaces a specified interior color. Both can be 4-connected or 8-connected. The document also discusses problems that can occur and more efficient span-based approaches.
The document describes the Breshenham's circle generation algorithm. It explains that the algorithm uses a decision parameter to iteratively select pixels along the circumference of a circle. It provides pseudocode for the algorithm, which initializes x and y values, calculates a decision parameter, and increments x while decrementing y at each step, plotting points based on the decision parameter. An example of applying the algorithm to generate a circle with radius 5 is also provided.
The depth buffer method is used to determine visibility in 3D graphics by testing the depth (z-coordinate) of each surface to determine the closest visible surface. It involves using two buffers - a depth buffer to store the depth values and a frame buffer to store color values. For each pixel, the depth value is calculated and compared to the existing value in the depth buffer, and if closer the color and depth values are updated in the respective buffers. This method is implemented efficiently in hardware and processes surfaces one at a time in any order.
Window to Viewport Transformation in Computer Graphics with.pptxDolchandra
The document discusses the window to viewport transformation process which maps a 3D world coordinate system to a 2D device coordinate system for display. It involves scaling, rotation, translation and clipping transformations. A window defines the region of the 3D world to view, while the viewport defines where on the display device this window will be mapped. The mapping from world coordinates within the window to device coordinates within the viewport involves coordinate system transformations. Zooming effects are achieved by changing the relative sizes of the window and viewport.
The Sutherland-Hodgman algorithm clips polygons by clipping against each edge of the clipping window in a specific order: left, top, right, bottom. It works by testing each edge of the polygon against the clipping window boundary and either keeping or discarding vertices based on whether they are inside or outside the window. The algorithm results in a clipped polygon that only includes vertices and edge intersections that are inside the clipping window.
The document discusses concepts related to basic illumination models. It covers key components like ambient light, diffuse illumination, and specular reflection that contribute to how objects are illuminated. It notes that illumination models try to approximate real world lighting in a realistic but not perfectly accurate way. The document also discusses challenges like accounting for all light rays reflected between nearby objects and having multiple light sources and viewing directions in a scene.
Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
There are two main types of projections: perspective and parallel. In perspective projection, lines converge to a single point called the center of projection, creating the illusion of depth. In parallel projection, lines remain parallel as they are projected onto the view plane. Perspective projection is more realistic but parallel projection preserves proportions. Perspective projections can be one-point, two-point, or three-point depending on the number of principal vanishing points. Orthographic projections use perpendicular lines while oblique projections are at an angle. Common parallel projections include isometric, dimetric, trimetric, cavalier and cabinet views.
3D transformation in computer graphicsSHIVANI SONI
This document discusses different types of 2D and 3D transformations that are used in computer graphics, including translation, rotation, scaling, shearing, and reflection. It provides the mathematical equations and transformation matrices used to perform each type of transformation on 2D and 3D points and objects. Key types of rotations discussed are roll (around z-axis), pitch (around x-axis), and yaw (around y-axis). Homogeneous coordinates are introduced for representing 3D points.
hidden surface elimination using z buffer algorithmrajivagarwal23dei
The document discusses hidden surface removal techniques used in 3D computer graphics. It introduces the hidden surface problem that arises when non-transparent objects obscure other objects from view. It describes object space and image space methods for identifying and removing hidden surfaces. The z-buffer algorithm is discussed as a commonly used image space method that works by comparing depth values in a z-buffer to determine which surfaces are visible at each pixel location.
This document discusses various visible surface detection methods in computer graphics. It describes object-space methods like back-face detection that compare object surfaces, and image-space methods like depth buffering that determine visibility point-by-point. Specific algorithms covered include depth buffering, scan-line, depth sorting, BSP trees, ray casting, and methods for curved and wireframe surfaces. It also provides examples and discusses functions for implementing visibility detection in OpenGL.
This document discusses various 3D transformations including translation, rotation, scaling, reflection, and shearing. It provides the transformation matrices for each type of 3D transformation. It also discusses combining multiple transformations through composite transformations by multiplying the matrices in sequence from right to left.
The document discusses the 2D viewing pipeline. It describes how a 3D world coordinate scene is constructed and then transformed through a series of steps to 2D device coordinates that can be displayed. These steps include converting to viewing coordinates using a window-to-viewport transformation, then mapping to normalized and finally device coordinates. It also covers techniques for clipping objects and lines that fall outside the viewing window including Cohen-Sutherland line clipping and Sutherland-Hodgeman polygon clipping.
Window to viewport transformation&matrix representation of homogeneous co...Mani Kanth
The document discusses window to viewport transformation and the use of homogeneous coordinates. A window defines the area of data to display, while a viewport defines where on the display device the window will appear. Window to viewport transformation maps the window coordinates to viewport coordinates using translation and resizing. Homogeneous coordinates represent points using an extra dimension, allowing rotation, scaling and other transformations to be represented using matrix multiplication.
with today's advanced technology like photoshop, paint etc. we need to understand some basic concepts like how they are cropping the image , tilt the image etc.
In our presentation you will find basic introduction of 2D transformation.
In a raster scan system, the electron beam scans across rows of the screen from top to bottom, turning intensity on and off to illuminate spots and form an image. The image definition is stored in a refresh buffer memory that holds intensity values for screen points. In a random scan system, an application and graphics package are stored in memory, and graphics commands are translated into a display file that a display processor accesses to refresh the screen. Graphics patterns are drawn by directing the electron beam along picture lines one at a time, positioning it between coordinate-defined endpoints to fill each line.
The document discusses different methods for 3D display and projection. It describes parallel projection, where lines of sight are parallel, and perspective projection, where lines converge at vanishing points. The key types of projection are outlined as parallel (orthographic and oblique) and perspective. Orthographic projection uses perpendicular lines, while oblique projection uses arbitrary angles. Perspective projection creates realistic size variation with distance and can have one, two, or three vanishing points.
The document discusses window to viewport transformation. It defines a window as a world coordinate area selected for display and a viewport as a rectangular region of the screen selected for displaying objects. Window to viewport mapping requires transforming coordinates from the window to the viewport. This involves translation, scaling and another translation. Steps include translating the window to the origin, resizing it based on the viewport size, and translating it to the viewport position. An example transforms a sample window to a viewport through these three steps.
This document discusses methods for identifying and removing hidden surfaces when rendering 3D scenes to create a realistic 2D image. It describes two approaches: object-space methods that compare whole objects, and image-space methods that decide visibility point-by-point. It focuses on the depth buffer/z-buffer method, which processes surfaces one point at a time, comparing depth values to determine visibility and store the color of visible points. It also discusses using scan line coherence to solve hidden surfaces one scan line at a time from top to bottom.
The document discusses several methods for visible surface detection or hidden surface removal in 3D computer graphics, including object space and image space methods. Object space methods determine visibility in 3D coordinates and include depth sorting and binary space partitioning (BSP) trees, while image space methods determine visibility on a per-pixel basis and include the depth-buffer or z-buffer method and ray casting. The depth-buffer method uses two buffers, a frame buffer and depth buffer, to render surfaces from back to front on a pixel-by-pixel basis. BSP trees recursively subdivide space with splitting planes to give a rendering order that correctly draws objects from back to front.
This document summarizes the scan-line rendering algorithm. It maintains two tables - an edge table containing line coordinates and surface pointers, and a polygon table containing surface properties. For each scan line, all intersecting surfaces are examined to determine the visible surface. Depths are calculated to set surface flags and populate the image buffer with intensity values from the visible surface. Coherence between scan lines is exploited to reuse prior visibility calculations where edge intersections remain the same.
The document describes different algorithms for filling polygon and area shapes, including scanline fill, boundary fill, and flood fill algorithms. The scanline fill algorithm works by determining intersections of boundaries with scanlines and filling color between intersections. Boundary fill works by starting from an interior point and recursively "painting" neighboring points until the boundary is reached. Flood fill replaces a specified interior color. Both can be 4-connected or 8-connected. The document also discusses problems that can occur and more efficient span-based approaches.
The document describes the Breshenham's circle generation algorithm. It explains that the algorithm uses a decision parameter to iteratively select pixels along the circumference of a circle. It provides pseudocode for the algorithm, which initializes x and y values, calculates a decision parameter, and increments x while decrementing y at each step, plotting points based on the decision parameter. An example of applying the algorithm to generate a circle with radius 5 is also provided.
The depth buffer method is used to determine visibility in 3D graphics by testing the depth (z-coordinate) of each surface to determine the closest visible surface. It involves using two buffers - a depth buffer to store the depth values and a frame buffer to store color values. For each pixel, the depth value is calculated and compared to the existing value in the depth buffer, and if closer the color and depth values are updated in the respective buffers. This method is implemented efficiently in hardware and processes surfaces one at a time in any order.
Window to Viewport Transformation in Computer Graphics with.pptxDolchandra
The document discusses the window to viewport transformation process which maps a 3D world coordinate system to a 2D device coordinate system for display. It involves scaling, rotation, translation and clipping transformations. A window defines the region of the 3D world to view, while the viewport defines where on the display device this window will be mapped. The mapping from world coordinates within the window to device coordinates within the viewport involves coordinate system transformations. Zooming effects are achieved by changing the relative sizes of the window and viewport.
The Sutherland-Hodgman algorithm clips polygons by clipping against each edge of the clipping window in a specific order: left, top, right, bottom. It works by testing each edge of the polygon against the clipping window boundary and either keeping or discarding vertices based on whether they are inside or outside the window. The algorithm results in a clipped polygon that only includes vertices and edge intersections that are inside the clipping window.
The document discusses concepts related to basic illumination models. It covers key components like ambient light, diffuse illumination, and specular reflection that contribute to how objects are illuminated. It notes that illumination models try to approximate real world lighting in a realistic but not perfectly accurate way. The document also discusses challenges like accounting for all light rays reflected between nearby objects and having multiple light sources and viewing directions in a scene.
Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
There are two main types of projections: perspective and parallel. In perspective projection, lines converge to a single point called the center of projection, creating the illusion of depth. In parallel projection, lines remain parallel as they are projected onto the view plane. Perspective projection is more realistic but parallel projection preserves proportions. Perspective projections can be one-point, two-point, or three-point depending on the number of principal vanishing points. Orthographic projections use perpendicular lines while oblique projections are at an angle. Common parallel projections include isometric, dimetric, trimetric, cavalier and cabinet views.
3D transformation in computer graphicsSHIVANI SONI
This document discusses different types of 2D and 3D transformations that are used in computer graphics, including translation, rotation, scaling, shearing, and reflection. It provides the mathematical equations and transformation matrices used to perform each type of transformation on 2D and 3D points and objects. Key types of rotations discussed are roll (around z-axis), pitch (around x-axis), and yaw (around y-axis). Homogeneous coordinates are introduced for representing 3D points.
hidden surface elimination using z buffer algorithmrajivagarwal23dei
The document discusses hidden surface removal techniques used in 3D computer graphics. It introduces the hidden surface problem that arises when non-transparent objects obscure other objects from view. It describes object space and image space methods for identifying and removing hidden surfaces. The z-buffer algorithm is discussed as a commonly used image space method that works by comparing depth values in a z-buffer to determine which surfaces are visible at each pixel location.
This document discusses various visible surface detection methods in computer graphics. It describes object-space methods like back-face detection that compare object surfaces, and image-space methods like depth buffering that determine visibility point-by-point. Specific algorithms covered include depth buffering, scan-line, depth sorting, BSP trees, ray casting, and methods for curved and wireframe surfaces. It also provides examples and discusses functions for implementing visibility detection in OpenGL.
This document discusses algorithms for visible surface determination (VSD) to determine which surfaces are visible during 3D rendering. It describes two main approaches: image precision, which operates at the display resolution, and object precision, which operates at the object level. It also discusses techniques like the depth buffer and depth sorting algorithms. The depth buffer method uses two buffers - a depth buffer and frame buffer - to track pixel depth and color values. It processes objects and surfaces, testing pixels and updating the buffers. Depth sorting paints surfaces in order of decreasing depth to resolve visibility.
3 d display-methods-in-computer-graphics(For DIU)Rajon rdx
3D computer graphics use three-dimensional representations of geometric data stored in a computer to render 2D images for later display or real-time viewing. This document discusses several 3D display methods in computer graphics including parallel projection, perspective projection, and depth cueing. Parallel projection projects points onto a plane along parallel lines, maintaining proportions but not producing realistic views. Perspective projection uses lines converging at a center point to give a more realistic impression of depth. Depth cueing varies the intensity of displayed objects based on distance to convey depth information.
This document discusses algorithms for hidden surface removal in 3D computer graphics. It describes two main classifications of algorithms - object space and image space. It then provides details on various algorithms including Painter's algorithm (object space), Z-buffer algorithm (image space), and Warnock's area subdivision algorithm. The key aspects and approaches of each algorithm are summarized.
Depth image recognition using isomorphic graph theoryChristian Kehl
This document discusses using graph theory and depth images to recognize objects. It proposes constructing a mesh of the world from depth camera data, transforming depth images into normal maps, and representing each region or plane as a different color "billboard". Objects in images can be matched by growing regions into nodes connected by edges between neighboring regions. Graphs of images could then be compared to find the largest isomorphic subgraphs and determine if the images match.
The document discusses various algorithms for visible surface detection, which is the identification and removal of surfaces that are not visible to the user based on their perspective. It describes the Z-buffer algorithm, BSP algorithm, A-buffer algorithm, scan-line algorithm, and painter's/depth sorting algorithm. For the Z-buffer algorithm, it explains how it uses two buffers (Z-buffer and refresh buffer) to compare depth values of overlapping pixels and determine which surfaces are visible. It also discusses considerations for different viewing directions. The BSP algorithm sorts polygons from back to front using a binary space partitioning tree. The A-buffer improves on Z-buffer for transparent surfaces by using linked lists at each pixel. The scan-line
The A-buffer method is an extension of the depth-buffer method that allows for anti-aliasing and transparency. It works by building a pixel mask for each polygon fragment and determining the visible areas to average color values. The key data structure is the accumulation buffer, which stores color, opacity, depth, coverage, and other data for each pixel. It operates similar to a depth buffer but also considers opacity to determine the final pixel color.
B. SC CSIT Computer Graphics Unit 4 By Tekendra Nath YogiTekendra Nath Yogi
The document discusses various techniques for visible surface determination and surface rendering in 3D graphics. It covers algorithms like z-buffer, list priority, and scan line algorithms for visible surface detection. It also discusses illumination models, surface shading methods like Gouraud and Phong shading, and provides pseudocode examples for image space and object space visible surface determination methods. Specific algorithms covered in more detail include the back face detection, z-buffer, list priority, and scan line algorithms.
This document provides an overview of machine vision techniques for region segmentation. It discusses region-based and boundary-based approaches to image segmentation. Key aspects covered include thresholding techniques, region representation using data structures like the region adjacency graph, and algorithms for region splitting and merging. Automatic threshold selection methods like the p-tile and mode methods are also summarized.
HIDDEN SOLID REMOVAL ALGORITHM IN COMPUTER GRAPHICS FOR IMAGE PROCESSING THEO...navneethsasikumar17
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This document discusses various techniques for image segmentation. It describes two main approaches to segmentation: discontinuity-based methods that detect edges or boundaries, and region-based methods that partition an image into uniform regions. Specific techniques discussed include thresholding, gradient operators, edge detection, the Hough transform, region growing, region splitting and merging, and morphological watershed transforms. Motion can also be used for segmentation by analyzing differences between frames in a video.
This document provides an overview of various image enhancement techniques. It begins with an introduction to image enhancement and its objectives. It then outlines and describes several categories of enhancement methods, including spatial-frequency domain methods, point operations, histogram operations, spatial operations, and transform operations. Specific techniques discussed in detail include contrast stretching, clipping, thresholding, median filtering, unsharp masking, and principal component analysis for multispectral images. The document also covers color image enhancement and techniques for pseudocoloring.
This document discusses different methods for visible surface determination in 3D computer graphics. It describes object-space methods that compare objects within a scene to determine visibility, and image-space methods that decide visibility on a point-by-point basis at each pixel. Specific methods mentioned include the back-face detection method, depth-buffer/z-buffer method, and A-buffer method. The depth-buffer method stores depth and color values in buffers for each pixel and compares surface depths to determine visibility. The A-buffer method extends this to allow accumulation of intensities for transparent surfaces.
There are two main categories of visible surface detection algorithms: object-space methods that compare objects in a 3D scene, and image-space methods that determine visibility on a per-pixel basis. The painter's algorithm sorts polygons by depth and draws more distant polygons before closer ones, covering some areas. The binary space partitioning algorithm draws polygons farther from the viewpoint before closer ones. Back face detection identifies whether a surface's normal vector points towards or away from the viewpoint.
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In Computer Graphics, Hidden surface determination also known as Visible Surface determination or hidden surface removal is the process used to determine which surfaces
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will also discuss Algorithm based on Z-buffer method, A-buffer method, and Scan-Line Method.
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2. Visible Surface Detection
●
Visible surface detection or hidden surface
removal.
●
Realistic scenes: closer objects occludes the
others.
●
Classification:
– Object space methods
– Image space methods
3. Object Space Methods
●
Algorithms to determine which parts of the shapes
are to be rendered in 3D coordinates.
●
Methods based on comparison of objects for their 3D
positions and dimensions with respect to a viewing
position.
●
For N objects, may require N*N comparision
operations.
●
Efficient for small number of objects but difficult to
implement.
●
Depth sorting, area subdivision methods.
4. Image Space Methods
●
Based on the pixels to be drawn on 2D. Try to
determine which object should contribute to that
pixel.
●
Running time complexity is the number of pixels
times number of objects.
●
Space complexity is two times the number of pixels:
– One array of pixels for the frame buffer
– One array of pixels for the depth buffer
●
Coherence properties of surfaces can be used.
●
Depth-buffer and ray casting methods.
5. Depth Cueing
●
Hidden surfaces are not removed but displayed with
different effects such as intensity, color, or shadow
for giving hint for third dimension of the object.
●
Simplest solution: use different colors-intensities
based on the dimensions of the shapes.
6. Back-Face Detection
●
Back-face detection of 3D polygon surface is
easy
●
Recall the polygon surface equation:
●
We need to also consider the viewing
direction when determining whether a
surface is back-face or front-face.
●
The normal of the surface is given by:
0<+++ DCzByAx
),,( CBA=N
7. Back-Face Detection
●
A polygon surface is a back face if:
●
However, remember that after application of
the viewing transformation we are looking
down the negative z-axis. Therefore a
polygon is a back face if:
0view >⋅NV
0ifor
0)1,0,0(
<
>⋅−
C
N
8. Back-Face Detection
●
We will also be unable to see surfaces with
C=0. Therefore, we can identify a polygon
surface as a back-face if:
0≤C
9. Back-Face Detection
●
Back-face detection can identify all the
hidden surfaces in a scene that contain non-
overlapping convex polyhedra.
●
But we have to apply more tests that contain
overlapping objects along the line of sight to
determine which objects obscure which
objects.
10. Depth-Buffer Method
●
Also known as z-buffer method.
●
It is an image space approach
– Each surface is processed separately one pixel
position at a time across the surface
– The depth values for a pixel are compared
and the closest (smallest z) surface
determines the color to be displayed in the
frame buffer.
– Applied very efficiently on polygon surfaces
– Surfaces are processed in any order
12. Depth-Buffer Method
●
Two buffers are used
– Frame Buffer
– Depth Buffer
●
The z-coordinates (depth values) are usually
normalized to the range [0,1]
13. Depth-Buffer Algorithm
●
Initialize the depth buffer and frame buffer so that
for all buffer positions (x,y),
depthBuff (x,y) = 1.0, frameBuff (x,y) =bgColor
●
Process each polygon in a scene, one at a time
– For each projected (x,y) pixel position of a polygon,
calculate the depth z.
– If z < depthBuff (x,y), compute the surface color at
that position and set
depthBuff (x,y) = z, frameBuff (x,y) = surfCol (x,y)
14. Calculating depth values efficiently
●
We know the depth values at the vertices.
How can we calculate the depth at any other
point on the surface of the polygon.
●
Using the polygon surface equation:
C
DByAx
z
−−−
=
15. Calculating depth values efficiently
●
For any scan line adjacent horizontal x
positions or vertical y positions differ by 1
unit.
●
The depth value of the next position (x+1,y)
on the scan line can be obtained using
C
A
z
C
DByxA
z
−=
−−+−
=′
)1(
16. Calculating depth values efficiently
●
For adjacent scan-lines we can compute the
x value using the slope of the projected line
and the previous x value.
C
BmA
z
m
xx
+
+=′⇒
−=′
/
z
1
18. Z-Buffer and Transparency
●
We may want to render transparent surfaces (alpha ≠1)
with a z-buffer
●
However, we must render in back to front order
●
Otherwise, we would have to store at least the first
opaque polygon behind transparent one
Partially
transparent
Opaque
Opaque 1st
2nd
3rd
Front
1st or 2nd
1st or 2nd
Must recall this
color and depth
3rd: Need depth
of 1st and 2nd
OK. No Problem Problematic Ordering
19. A-Buffer Method
●
Extends the depth-buffer algorithm so that
each position in the buffer can reference a
linked list of surfaces.
●
More memory is required
●
However, we can correctly compose different
surface colors and handle transparent
surfaces.
20. A-Buffer Method
●
Each position in the A-buffer has two fields:
– a depth field
– surface data field which can be either surface
data or a pointer to a linked list of surfaces
that contribute to that pixel position
21. Scan Line Method
●
Extension of the scan-line algorithm for filling
polygon interiors
For all polygons intersecting each scan line
Processed from left to right
Depth calculations for each overlapping
surface
The intensity of the nearest position is entered
into the refresh buffer
22. Tables for The Various Surfaces
Edge table
Coordinate endpoints for each line
Slope of each line
Pointers into the polygon table
o
Identify the surfaces bounded by each line
Polygon table
Coefficients of the plane equation for each surface
Intensity information for the surfaces
Pointers into the edge table
23. Active List & Flag
Active list
Contain only edges across the current scan line
Sorted in order of increasing x
Flag for each surface
Indicate whether inside or outside of the surface
At the leftmost boundary of a surface
The surface flag is turned on
At the rightmost boundary of a surface
The surface flag is turned off
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