International Business Machines Corporation

Koji Koyamada

Akio Doi

Sakae Uno

Tatsuo Miyazawa

Takayuki Ito

Takayuki Itoh

Gregory P Bala

According to the present invention, a method is provided for assigning or converting volume data values defined at the center of cells to volume data values at node points, considering the residuals. Volume data values at a plurality of node points are computed from a volume data value at a center of each of a plurality of cells which are composed of the plurality of node points, where the position and the ID of each node point are stored in a memory with relation to each corresponding node point, and the volume data value at each node point is computed so that a value determined by (a) weighting a residual value which is the difference between a cell-inside value at a point inside a cell and a volume data value at the center of the cell by a predetermined weighting function, where the cell-inside value is calculated by interpolating a volume data at each node point which composes the cell, and then (b) accumulating the weighted residual value over all regions of the cell for each of the plurality of cells and (c) summing up the accumulations, is set to zero.

Method and apparatus for computing and visualizing volume data values

A rendering method is provided that can materialize rendering processing from volume data at high speed using a surface rendering processor without restrictions on the structure of volume data to be processed. In the method, the sampling points of volume data V over a 3-D region are, in principle, arranged on the surfaces Q.sub.1, Q.sub.2, . . . Q.sub.n in equal intervals along a viewing ray L around viewing point p, and these surfaces are extracted as a set of triangles T.sub.i. Then, the volume data at each vertex of these triangles and the gradient vectors of this data are obtained by interpolation and generated as a triangle data group. High-speed volume rendering is materialized by displaying the data groups of these partially transparent triangles using a surface rendering processor. Since existing programs can be used for generation and processing of triangle data groups, there are no restrictions on the structure of the volume data to be handled.

Method and device for volume rendering using concentric spherical

A method and apparatus for displaying stream lines in a space are disclosed. First, the space is divided into a plurality of tetrahedral cells. Position data of each vertex of the tetrahedral cells and vector data at each position are collected. A critical point for each tetrahedral cell is then computed. The critical point is within the tetrahedral cell and for which the vector data becomes zero. Using the collected position and vector data, a Jacobian matrix J is calculated when such a critical point is found, and eigenvalues of the Jacobian matrix J are also calculated. Next, the starting point of a stream line within a tetrahedral cell is calculated for each of the eigenvalues by moving a microscopic distance from the critical point. Finally, a stream line is calculated from the starting point, and the stream line is displayed.

Method and system for displaying vector data as stream lines in a space

To provide high-speed volume rendering without computing the points at which a viewing ray intersects with the boundaries of a volume data area. Visualizing a volume entails: selecting the exterior faces that face toward a viewing point from among a plurality of exterior faces of a volume data area, sorting the ones thus selected according to distance from the viewing point, selecting those exterior faces in the sorting order, and determining pixels on a projection plane corresponding to the exterior faces in question by scan conversion; computing pixel values along each viewing ray passing through each pixel for each corresponding exterior face until a final exterior face is encountered; such a final exterior face can be judged from information on many partial solids restricting the volume data area; when a viewing ray enters the volume data area again, pixel values to be added later on another exterior face are computed and added to the previous pixel values; the completion of processing of all exterior faces facing toward a viewing point is tantamount to the completion of processing all viewing rays.

Data visualizer utilizing exterior selected and depth sorted polyhedron

An isosurface is composed of grid points having a predetermined scalar value. The method and apparatus of the present invention generates an isosurface by extracting from volume data a first grid point having a minimum scalar value and a second grid point having a maximum scalar value. A list of polyhedrons that intersect a line connecting the first grid point to the second grid point is generated and stored. The isosurface is generated in accordance with the list of polyhedrons and the predetermined scalar value. Because the volume data obtained by scientific and technological calculation or the like is kept in the form of a polyhedron list having an associated maximum scalar value and minimum scalar value, generating an isosurface according to a predetermined scalar value can be accomplished at high speed.

Method and apparatus for generating isosurfaces

Methods and apparatus are provided for generating isosurfaces, given input data that includes (1) the representation of a set of points in three-dimensional space; (2) connectivity information with respect to the set of points and (3) a scalar field. The methods and apparatus allow the desired isosurfaces to be produced efficiently on all hardware platforms, including those not equipped to rapidly generate such isosurfaces using normally computation intensive processes, by utilizing a precomputed isofacet configuration table and predefined tetrahedron component labeling data (preset relationships among the vertices, edges and faces of a tetrahedron). Further aspects of the methods and apparatus include (1) methods and apparatus which support the selective display of isosurface and contour line images, and (2) methods and apparatus which utilize parallel processing techniques to enhance the efficiency of the isosurface generation process.

Methods and apparatus for efficiently generating isosurfaces and for

Portions showing greater specular reflection of an object to be displayed are displayed with pixels whose opacity, .alpha..sub.1, is emphasized according to the specular reflected component of a shading model, in which case the specular reflected component thus calculated for shading is also utilized for arithmetic operation of emphasized opacity, .alpha..sub.1, and high-speed processing is sought through tabulating various variables such as .alpha..sub.s (an additional opacity introduced for emphasis by a specular reflected component), .alpha..sub.n (a primary opacity), and G (a gradient vector).

Volume rendering method which increases apparent opacity of

A method and apparatus for generating image data representing an iso-valued surface. A series of points in three dimensional space each having positional data and an assigned scalar value is analyzed by dividing the space into tetrahedral elements, generating tetrahedral element representative normal vectors, generating vertex representative normal vectors data, and calculating pixel values for viewing rays passing through the tetrahedra. Tetrahedral elements have the advantage of requiring only the solution of linear equations instead of quadratic equations. The use of representative normal vector data rather than geometric data for each associated triangle greatly reduces the storage requirements for processing the data. The reduced data storage and associated reduced processing time allows generation of iso-valued surfaces at high speed with a minimum memory requirement.

Growing community of inventors

Hadano, Japan

Koji Koyamada