Embedded minimal surfaces, computer graphics and elliptic functions

1985 ◽  
pp. 204-215 ◽  
Author(s):  
David Hoffman
Keyword(s):  
Computer Graphics ◽  
Minimal Surfaces ◽  
Elliptic Functions

Computer graphics tools for the study of minimal surfaces

1988 ◽  
Vol 31 (6) ◽  
pp. 648-661 ◽  
Author(s):  
M. J. Callahan ◽  
D. Hoffman ◽  
J. T. Hoffman
Keyword(s):  
Computer Graphics ◽  
Minimal Surfaces

A ONE-PARAMETER FAMILY OF MINIMAL SURFACES WITH FOUR PLANAR ENDS

1995 ◽  
Vol 06 (02) ◽  
pp. 149-159 ◽  
Author(s):  
FARUK F. ABI-KHUZAM
Keyword(s):  
Minimal Surfaces ◽  
Total Curvature ◽  
Elliptic Functions ◽  
Parameter Family ◽  
Explicit Formulas ◽  
Jacobian Elliptic Functions ◽  
Genus One

Using Jacobian elliptic functions we construct a one-parameter family of regular complete minimal surfaces of genus one with total curvature – 16π and having four embedded planar ends. The explicit formulas obtained reveal that two ends are asymptotic to one and the same plane.

Improved 3-D reconstruction using stereo computer graphics and multiple tilt EM images

1995 ◽  
Vol 53 ◽  
pp. 630-631
Author(s):  
Lee D. Peachey ◽  
Lou Fodor ◽  
John C. Haselgrove ◽  
Stanley M. Dunn ◽  
Junqing Huang
Keyword(s):  
Computer Graphics ◽  
High Performance ◽  
Transverse Section ◽  
Three Dimensional ◽  
Stereo Pair ◽  
3D Reconstructions ◽  
Video Cameras ◽  
Biological Objects ◽  
Microscope Images ◽  
High Performance Computer

Stereo pairs of electron microscope images provide valuable visual impressions of the three-dimensional nature of specimens, including biological objects. Beyond this one seeks quantitatively accurate models and measurements of the three dimensional positions and sizes of structures in the specimen. In our laboratory, we have sought to combine high resolution video cameras with high performance computer graphics systems to improve both the ease of building 3D reconstructions and the accuracy of 3D measurements, by using multiple tilt images of the same specimen tilted over a wider range of angles than can be viewed stereoscopically. Ultimately we also wish to automate the reconstruction and measurement process, and have initiated work in that direction.Figure 1 is a stereo pair of 400 kV images from a 1 micrometer thick transverse section of frog skeletal muscle stained with the Golgi stain. This stain selectively increases the density of the transverse tubular network in these muscle cells, and it is this network that we reconstruct in this example.

Stereo modeling of HVEM specimens by serial tilting and computer graphics

1986 ◽  
Vol 44 ◽  
pp. 34-35
Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway
Keyword(s):  
Computer Graphics ◽  
Analytical Methods ◽  
Photographic Film ◽  
Complex Structures ◽  
Multiple Objects ◽  
Multiple Images ◽  
3 Dimensional

EM specimens often contain 3-dimensional information that is lost during micrography on a single photographic film. Two images of one specimen at appropriate orientations give a stereo view, but complex structures composed of multiple objects of graded density that superimpose in each projection are often difficult to decipher in stereo. Several analytical methods for 3-D reconstruction from multiple images of a serially tilted specimen are available, but they are all time-consuming and computationally intense.

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