Computer Graphics: Visible surface detection methods

Visible-Surface Detection Methods

Outline of Presentation

1. Introduction2. Classification3. Depth-Buffer Algorithm

1. Introduction

• A set of 3-D surfaces are to be projected onto a 2-D screen.

• To identify those parts of a scene that are visible from a chosen viewing position.

• Correct visibility – when multiple opaque polygons cover the same

screen space, only the closest one is visible.

Visibility

• There are many algorithms developed and still being developed for visible surface detection or Hidden surface removal.

• Characteristics of approaches:– Require large memory size.– Require long processing time.– Applicable to which types of objects?

• Considerations:– Complexity of the scene– Type of objects in the scene– Available equipment– Static or animated?

• Visible-surface detection methods and hidden-surface elimination methods are similar but distinct.

2. Classification

• Visible-surface detection algorithms are broadly classified into 2 types.1. Object –space methods2. Image-space methods

Object-space methods

• Deals with object definitions directly.• Compare objects and parts of objects to each

other within the scene definition to determine which surfaces, as a whole, we should label as visible.

• It is a continuous method.• Compare each object with all other objects to

determine the visibility of the object parts.

Pros and Cons of Object-space Methods

• If there are n objects in the scene, complexity = O(n2)

• Calculations are performed at the resolution in which the objects are defined (only limited by the computation hardware).

• Process is unrelated to display resolution or the individual pixel in the image and the result of the process is applicable to different display resolutions.

• Display is more accurate but computationally more expensive as compared to image space

• methods are typically more complex, due to the possibility of intersection between surfaces.

• Suitable for scene with small number of objects and objects with simple relationship with each other.

Image Space methods

• Deals with the projected images of the objects and not directly with objects.

• Visibility is determined point by point at each pixel position on the projection plane.

• It is a discrete method.• Accuracy of the calculation is bounded by the

display resolution.• A change of display resolution requires re-

calculation

Two main strategies

• 1. Sorting• 2. Coherence

1. Sorting– Sorting is used to facilitate depth comparisons by

ordering the individual surfaces in a scene according to their distance from the view plane.

Coherence

• Making use of the results calculated for one part of the scene or image for other nearby parts.

• Coherence is the result of local similarity• As objects have continuous spatial extent,

object properties vary smoothly within a small local region in the scene.

• Calculations can then be made incremental.

3. Depth-Buffer Method (Z-Buffer Method)

• It is a commonly used image-space approach to detecting visible surfaces proposed by Catmull in 1974.

• It compares the surface depths at each pixel position on the projection plane.

• Object depth is usually measured from the view plane along the z axis of a viewing system.

• Each surface of a scene is processed separately, one point at a time across the surface.

• This method requires 2 buffers:1) Depth buffer or z-buffer: • To store the depth values for each (X, Y)

position, as surfaces are processed.• 0 ≤ depth ≤ 12) Refresh Buffer or Frame Buffer:• To store the intensity value or Color value at

each position (X, Y).

Algorithm

1. depthbuffer(x,y) = 0framebuffer(x,y) = background color

2. Process each polygon one at a time2.1. For each projected (x,y) pixel position of a polygon, calculate depth z.2.2. If z > depthbuffer(x,y)

compute surface color, set depthbuffer(x,y) = z, framebuffer(x,y) = surfacecolor(x,y)

Example

• The Final Image

Z = 0.3

Z = 0.5

• Step 1: Initialize the depth buffer

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

• Step 2: Draw the polygon with depth 0.3 (2.2)

0 0 0 0

0 0 0 0

0.3 0.3 0 0

0.3 0.3 0 0

• Step 3: Draw the polygon with depth 0.5

0 0 0 0

0 0.5 0.5 0

0.3 0.5 0.5 0

0.3 0.3 0 0

Calculating Depth

• We know the depth values at the vertices. • we can calculate the depth at any other point

on the surface of the polygon using the polygon surface equation:

C

DByAxz

• 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

Az

C

DByxAz

)1(

• For adjacent scan-lines we can compute the x value using the slope of the projected line and the previous x value.

C

BmAz

mxx

/z

1

Pros and Cons

• Widely used• Simple to implement• Needs large amount of memory (uses 2

buffers)• Aliasing problem.• Handle only opaque surfaces• Problem when too many surfaces are there.

Questions

2 marks• What is the task of visible detection methods?• What is correct visibility?• What are the types of visible detection

algorithms?• Difference between object space methods and

image space methods?

• What are the two strategies used in visible surface detection algorithms?

• What is coherence in image space methods?• Mention two advantages of object space

method.• Mention two disadvantages of object space

method.• What are the disadvantages of Image space

method?

• What are the buffers used in Depth buffer method?

• What is the content of Z-buffer?• What is the content of refresh buffer?• What are the initial values of depth buffer and

refresh buffer?• What is the range of depth used in depth

buffer method?

• What is the equation to calculate depth value z at (x,y) for a polygon surface?

• Mention any two disadvantages of depth buffer method.

10 marks• Explain depth buffer method in detail.

Quote

If you have a ‘why’ to live for, you can cope with any ‘how’.

Thank you!