By Glen. Mullineux
Intersection of hetero line segments 103 Non-linearity and the intersection of curves 109 Subdivision and box-testing options 114 Closed curves a hundred and twenty an information constitution for closed curves 123 The merging of closed curves one hundred twenty five bankruptcy five: illustration of surfaces 133 advent 133 governed surfaces 134 Coons' patches 136 Surfaces via given issues 141 Bezier floor patches 143 B-spline surfaces 148 The DUCT approach 149 difficulties all in favour of placing patches jointly 153 bankruptcy 6: MODCON: an instance approach 159 heritage to the method 159 using primitive shapes one hundred sixty placing primitives jointly one hundred sixty five an easy instance one hundred seventy Operation of the method 171 boundaries of the process 174 Conclusions 176 bankruptcy 7: advent to floor and strong modelling 177 creation 177 forms of geometric modeller 177 good modelling 181 acquiring volumetric houses 186 Defining primitive volumetric shapes 188 Hidden line removing and floor shading a hundred ninety References 197 Index 199 bankruptcy 1 assessment of a few easy rules creation the aim of this bankruptcy is to study a few of the ordinary notation and ideas that underlie the cloth to be awarded later. those are the tips of arithmetic and of numerical arithmetic. they're very important from a working laptop or computer aided layout (CAD) viewpoint as the basically method within which we will be able to convince a working laptop or computer procedure to house geometry for us is through lowering it to a collection of numbers which could then be kept and manipulated.
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Additional info for CAD: Computational Concepts and Methods
The first angle represents a rotation about the current vertical axis. 8 Observer coordinate system through an angle > about a line in the horizontal plane as shown in the figure. These two angles are used to define the position of the observer and his line of sight is from this position to the origin. -:'L "'-.! os>J! inO + sin>J! n¢ coso cos>J! coso + sin>J! sin", sinO -sin>J! cos¢ [ -sm>J! smO - cos>J! sm¢ coso sin>J! cos 0 - cos>J! sin¢ sinO cos>J! 9 shows the types and order of viewing transformation that can be applied to a point or collection of points forming a complete shape.
59 CAD: Computational Concepts and Methods We present ways for dealing with curve shapes on a more or less historical basis, beginning with the classical Cartesian geometry approach to the study of curves and moving on to the more recent use of parametric forms such as Bezier and B-spline curves. Implicit equations From a Cartesian coordinate geometry viewpoint, we would describe a circle by an equation of the form: x2 + y2 = a2 and a parabola by one of the form: y2 = 4ax These are both planar curves.
J::. VI Xo link 0 link 0 QyO X4 link 5 Xs link 6 X6 Z6 ~6 '~~; . 14 Axes for a PUMA type robot X3 . / Z2 ~ '" 1:1- o ~ ;. - § ~ g. o C"l C"l Datastructures and transfonnations take Zi to be along the axis of rotation; select xi to be perpendicular to both Zi and Zi-I ; select Yi to be perpendicular to both Xi and Zi to form a right handed set of axes. 14. Note that the selection above ensures that relative to Fi as it moves with link i, the Zi-I axis appears fixed. We now look at the geometry of the robot and consider how to transform frame Fi to bring it on top of frame F i - I .
CAD: Computational Concepts and Methods by Glen. Mullineux