Uday G. Gujar

3-D objects from 2-D orthographic views—A survey

Abstract The topic of generation of a solid 3-D object from given 2-D orthographic views has been studied for a number of years. In this paper we comment on the eleven papers published between 1973 to 1984 on this topic. Relevant features of these algorithms have been given in a comprehensive table form. A categorization tree based upon the various capabilities has been included.

Fractals from z ← zα + c in the complex c-plane

Abstract The self-squared function z ← z 2 + c , has been discussed extensively in the literature for generating fractals. In this article, we consider the generalized transformation function z ← z α + c for generating fractal images. A multitude of interesting, intriguing, and rich families of fractals are generated by changing a single parameter α. Direct relationships are observed between α and the visual characteristics of the fractal images in the c -plane. The exponent α can be represented as α = ± ( η + ϵ ), where η and ϵ are the integer and fractional parts, respectively. It is found that when α is a positive integer number, the resulting image contains lobular structures. The number of major lobes equals ( η − 1). When α is a negative integer number, the generated fractal image is a planetary structure consisting of overlapping central planets surrounded by satellite structures. The number of satellite structures equals ( η + 1). A continuous variation of α between two consecutive integers results into a continuous proportional change between the two limiting fractal images. Several conjuctures about the visual characteristics of the images and the value of α are stated.

Construction of 3D solid objects from orthographic views

Abstract An algorithm to generate three-dimensional solid objects, made up of planar surfaces, from the given three conventional engineering orthographic views is presented in this paper. Consisting of six major steps, the algorithm has been programmed in C on IRIS 1400 graphics workstation. The algorithm generates all possible solutions. The infinite space has been divided into finite subspaces by making use of the surface normals and the direction of travel of the edges that connect the faces. Classification of the probable 3D subobjects into the certain and uncertain ones has proved to be very useful in reducing the time taken by the algorithm. Several illustrative examples, simple as well as complex giving single and multiple solutions, are included.

Fractal images from z ← zα + c in the complex z-plane

Abstract The transformation function z ← zα + c is used for generating fractal images in the complex z-plane. When α is a positive integer the fractal image has a lobular structure with α major lobes. When α is a negative integer the image has a planetary configuration consisting of a central planet with |α| major satellite structures. For noninteger values of α, additional embryonic lobular/satellite structures, proportional in size to the fractional part of α, are observed. Based on the extensive experimentation, six conjectures regarding the number of major as well as embryonic lobular/satellite structures, their positions, and angular spaces are formulated.

A device independent computer plotting system

This paper describes a computer plotting system which is completely device independent. The user can switch from one plotting device to another without any programming changes. The interface for adding new plotting devices is formalized and discussed. The addition of a new plotting device is completely transparent to the user; in fact, the old programs may be used to produce plots on the new device without any programming changes whatsoever. The system was designed and implemented by the author in late 1971 and has been in use ever since (see Ref. 1). Several new plotting devices, real as well as pseudo, have been added successfully without affecting the users of the system.

Vectorization of generation of fractals from z ← z2 + c on IBM 3090/180VF

Abstract Algebraic fractals generated from the self-squared transformation function z ← z 2 + c , where z and c are complex quantities, have been discussed extensively in the literature. The process of generating these fractal images, being iterative in nature, is computationally intensive. In this paper we propose and study three vectorization techniques for generating algebraic fractals from z ← z 2 + c , namely, use of long vectors, short vectors, and short vectors with replenishment. The speedups obtained by vectorization of all these techniques on IBM 3090-180VF, which has a vector facility, are presented. It is observed that the technique of using short vectors with replenishment is the best.

A flexible software character generator

This paper describes a general and flexible character generator which is capable of producing virtually an unlimited number of character founts. To demonstrate this flexibility, eight different founts, ranging from Roman letters and symbols, double line letters, APL characters etc. to a Devanagari script have been generated. These founts have been chosen to see how characters with wide ranging requirements can be generated.

FORTRAN routines with optional arguments

In designing a general purpose subroutine package to solve a class of problems, one often has to write subroutines with a large number of arguments. Although these arguments are required to cover a range of possibilities, many of these arguments have some commonly occurring values. The user is thus burdened with supplying a long list of arguments and making sure that the number and types match. An alternate solution is to write such subroutines in assembly language so that they could have a variable number of arguments. This approach is expensive and eliminates a large class of program designers who do not and do not want to know assembler language. This paper describes a facility which enables these program designers to write their routines completely in a higher level language (FORTRAN) and yet enjoy the ‘luxury’ of having a variable number of arguments in the calling sequence.

Julia sets of z←z ∞ +c

The fractal images generated from the generalized transformation function z ←zα + c in the complex z-plane are analysed. The exponent a can assume any real or integer, either positive or negative, value. When the exponent α is a positive integer number, the fractal image has a lobular structure with number of lobes equal to α. When α is a negative integer number, the generated fractal image has a planetary structure with a central planet and ¦α¦ satellite structures around it. When α is varied continuously between two consecutive integer numbers, continuous and predictable changes are observed between the two limiting fractal images. Some conjectures regarding the visual characteristics of the fractal images and the value of α are included.

Interpolation techniques for 3-D object generation

Abstract The technique of interpolation (or blending) and its generalization is considered in this paper. A unifying model for generating 3-D objects using this technique is presented. Various factors which affect the shape of generated objects are identified. Several illustrative examples of 3-D objects generated by this technique, using linear as well as non-linear interpolation, are presented. Although many of the objects have complex shapes, they are represented by simple closed form mathematical equations.