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The textbook provides both beginner and experienced CAD users with
the math behind the CAD. The geometry tools introduced here help
the reader exploit commercial CAD software to its fullest extent.
In fact, the book enables the reader to go beyond what CAD software
packages offer in their menus. Chapter 1 summarizes the basic
Linear and Vector Algebra pertinent to vectors in 3D, with some
novelties: the 2D form of the vector product and the manipulation
of "larger" matrices and vectors by means of block-partitioning of
larger arrays. In chapter 2 the relations among points, lines and
curves in the plane are revised accordingly; the difference between
curves representing functions and their geometric counterparts is
emphasized. Geometric objects in 3D, namely, points, planes, lines
and surfaces are the subject of chapter 3; of the latter, only
quadrics are studied, to keep the discussion at an elementary
level, but the interested reader is guided to the literature on
splines. The concept of affine transformations, at the core of CAD
software, is introduced in chapter 4, which includes applications
of these transformations to the synthesis of curves and surfaces
that would be extremely cumbersome to produce otherwise. The book,
catering to various disciplines such as engineering, graphic
design, animation and architecture, is kept discipline-independent,
while including examples of interest to the various disciplines.
Furthermore, the book can be an invaluable complement to
undergraduate lectures on CAD.
The textbook provides both beginner and experienced CAD users with
the math behind the CAD. The geometry tools introduced here help
the reader exploit commercial CAD software to its fullest extent.
In fact, the book enables the reader to go beyond what CAD software
packages offer in their menus. Chapter 1 summarizes the basic
Linear and Vector Algebra pertinent to vectors in 3D, with some
novelties: the 2D form of the vector product and the manipulation
of "larger" matrices and vectors by means of block-partitioning of
larger arrays. In chapter 2 the relations among points, lines and
curves in the plane are revised accordingly; the difference between
curves representing functions and their geometric counterparts is
emphasized. Geometric objects in 3D, namely, points, planes, lines
and surfaces are the subject of chapter 3; of the latter, only
quadrics are studied, to keep the discussion at an elementary
level, but the interested reader is guided to the literature on
splines. The concept of affine transformations, at the core of CAD
software, is introduced in chapter 4, which includes applications
of these transformations to the synthesis of curves and surfaces
that would be extremely cumbersome to produce otherwise. The book,
catering to various disciplines such as engineering, graphic
design, animation and architecture, is kept discipline-independent,
while including examples of interest to the various disciplines.
Furthermore, the book can be an invaluable complement to
undergraduate lectures on CAD.
Performance indices and design charts can be used to quickly model
and compare the structural efficiency of different shaped
materials, layered systems and structural forms. This work presents
a method for modelling the mass-efficiency of structures at the
conceptual stage of design. The method is based on the concept of
shape transformers, which describe dimensionless shape properties
of a cross-section Shape transformers are size-independent and
practical for defining classes of shapes in a way which is similar
to the manner in which materials are classified. Used to formulate
performance indices for lightweight shaped materials with
arbitrarily scaled cross-sections and for plastic analysis of
beams, shape transformers are conducive to visualize the effect of
cross-section geometry and layer arrangement via material charts.
These geometric operators help also to visualize the interaction
between the selection of alternative structural forms and the
choice of constituent member cross-section shapes. The method
described here provides insight for engineers, students and
educators involved in lightweight structural design.
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