Fast perspective projection volume navigation [] []

In this paper they are using Frame-to-Frame coherence and another rendering method. Based in a previous work that was just for parallel projection. It is useful for external views since the distance from the viewer to the data is relatively large but it is not useful to go inside the volume where the viewer is inside the data.

Previous statements

It is supposed that the volume is isotropic. The sampling distance is . All the units in the paper are written in units of the voxel spacing .

The view frustum :

• Size of the view frustum volume.
• View frustum position and orientation is defined by position p and with an orientation .
• Depth of view is fixed d.
• An arbitrary path is traced through the volume and is defined by a discrete sequence of viewing sites where whose values are not known in advance.
• The path is sequence of incremental steps in a direction or rotations about an axis.

The coherence between nearby frames f is used.
The results from the computation of a given view are used to compute f successive frames, after which a refresh view must be produced. Sampling is obtaining the color and opacity of a point in the ray. (Interpolation, Transfer functions mapping, and shading or light calculation).
Composition is Volumetric composition equation in a front to back.
The algorithm is divided in 2 phases.

Phase 1

(figure ): Short ray segments are cast composite color computing the composite color and transparency for each segment.
Assumed that the sampling rate is for simplicity.

• The sample points are divided into L levels where based on the distance from the viewpoint.
• distance of the first sample of level l.
• Each level l consist of a set of ray segments or that treat the samples from to ( samples).
• or
• Result phase 1 L two-dimensional arrays.
• Each level can be sampled at different resolutions.
  horizontal and vertical resolutions of the segments casts in level l.
  With that they can get adaptive sampling to avoid undersampling of distance points. Trying to maintain similar lateral sampling.
  Avoid oversampling in the regions near the viewpoint. The few levels near the view point cast very few rays /it Acceleration.

  
Figure: 2D illustration of the segments computed by the two-phase algorithm. The horizontal lines represent the rectangles into which the segments are to be mapped

Phase 2

Construct approximations of the full rays in the second phase.

• do from to Screen resolution.
• alpha blending

Done using 2D-texture-Mapping for each level (acceleration hardware).

• Define a rectangle for any level
• Drawn with mapped at distance perpendicular two the view direction and from front to back and Alpha blending.
• Special treatment of Drawn between 0 and .

or from l=0 to l=L-2 resampling level l from to and composing with level l+1. not used

Performance

• Brute force raycasting is an special case of two-phase algorithm in which are cast to Depth d in a single level.
• 10 Levels and 0.385 times as many sample steps as the brute force approach. See table 1 in figure .
• Composing operation is nonlinear reordering interpolation and the composite steps will incur some error. See figure to do a visual comparison between brute force and two phase ray casting.

  
Figure: Rendering comparison: a) Brute force perspective raycasting. b) The two phase algorithm. c) Difference between the two multiplied by 10.

  
Figure: Tables of times and comparisons

Interactive Navigation

: Phase 1 can be reused to approximate frames from viewpoint near the base position (the position from where the phase 1 was calculated).

• radius from the base position.
• angle of the original viewing direction.
• levels that need to be recalculated in every step. So reused .

To avoid jerky motion due to the periodic pause to fresh the samples when the view position is out of . New position of refresh can be estimated (long translations in a direction or rotations about an axis) and spread it during the frames calculation.

Viewpoint Translation.

(See figure ).given

• is the position increment .
• next predicted structure. Computing of it in any step.
• The first levels move with viewpoint.
• The depth of levels varies by the amount .

    
  Figure: 2D description of the forward translation
  

• For each step one plane of samples should be rendered onto the back of the last level so that the total viewing depth remain the same.
• Calculate an slightly larger field of view for the positions behind the frustum.
• Fixed . Higher f less quality.

    
  Figure: 2D illustration of the resampling of S during translation
  

  PROBLEM It implies bigger and this implies the orientation of the S on the periphery of the view do not match.( See figure )
  The new segment s is bilaterally interpolated by the 4 segments nearest to s which is not parallel to the 4. Which are the weights distance of the interpolation?
  SOLUTIONS Average Distance or the resampling depends upon relative distance within the plane of the rectangle. Towards the edges the weighting is closer to the middle of the segments. In the middle distances are based on the position of the front.

Viewpoint Rotation

(figure )given

  
Figure: The initial segment data structure is depicted in gray and should be 2 wider that the field of view

• incremental in angle rotation in a axes.
• the size of the viewing frustum in the direction of rotation is wider.
• is the next predicted structure.
• levels from 0 to don't need to be recomputed at each step.
• More resampling accuracy than translation. No error in the orientation of the segments. Relative distance are well defined.

Times

See table 2 in figure ) in order to compare time savings.

  
Figure: Tables of times and comparisons