By Georg Glaeser
Overview initially of 1999, Springer-Verlag released the booklet Open Geo- test OpenGL +Advanced Geometry. There, the authors Georg Glaeser and Hellmuth Stachel awarded a entire library of geometric me- odsbasedonOpenGLroutines.AnaccompanyingCD-ROMprovidedthesource code and plenty of pattern ?les. Many various issues are coated during this e-book. The theoretical heritage is punctiliously defined, and lots of examples are given. because the booklet of Open Geometry, the resource code has been more desirable andmanyadditionalfeatureshavebeenaddedtotheprogram.Contributorsfrom allovertheworldhavecomeupupwithnewideas,questions,andproblems.This approach has persevered as much as the current and Open Geometry is starting to be from daytoday. with a purpose to make all of those advancements obtainable to the general public, and likewise with a purpose to provide deeper perception into Open Geometry, we made up our minds to write down this new instruction manual on Open Geometry GL 2.0. it is going to ?ll yes gaps ofOpen Geometry 1.0 and clarify new equipment, suggestions, and examples. at the accompanying CD-ROM the recent resource code and the pattern ?les are integrated. The guide now comprises one hundred and one well-documented examples and the reader is ready to know about Open Geometry through operating via them. additionally, we current a compendium of all vital Open Geometry periods and their equipment. vi Preface even if, we didn't intend to jot down a brand new educational for Open Geometry. The guide is very a sequel, written for the readers of the ?rst e-book and for advancedprogrammers.Furthermore,itisasourceofcreativeandgoodexamples from diversified ?elds of geometry, special effects, and lots of different similar ?elds like physics, arithmetic, astronomy, biology, and geography.
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Extra info for Handbook of Geometric Programming Using Open Geometry GL
Example text
Of course, you are right, but it would not be Open Geometry if it did not solve the same tasks in 3D – and that more or less by simply replacing all occurrences of 2d by 3d. Naturally, points in 3D should be initialized with three coordinates, and the point C must now rotate about the circle’s axis. Finally, a 3D projection instead of a 2D window has to be initialized. cpp"! , the function StraightLine3d(. . ) clearly draws a straight line in 3D, and the function MarkAngle(. . ) draws an arc in 3D when the parameters are space points P3d.
7. Torus as locus of space points with constant angle at circumference. 7): The locus of all space points from which a line segment AB is seen under constant angle at circumference γ is a torus. cpp". cpp", you will soon understand the code. 4. Draw( MEDIUM ) ; Obviously, a new class StrL3d – a straight line in 3D as a geometric object with member functions like Def(. . ) – is used. The 3D circle Circ3d can now be rotated about the axis AB. The axis can also be used to generate a parallel circle on the torus.
The same holds for all special curves in the following text. 6. 6). 3 By “neighboring” we mean two normals that are sufficiently close ; the real constant eps serves to define this term. 4 This is more or less a “geometric construction” of the evolute. Open Geometry’s philosophy aims at avoiding complicated computations. Instead, the user should immediately transfer geometric ideas to the program file. 42 Chapter 2. 6. The law of reflection. If you reflect the lines of a pencil with vertex E on c, the reflected lines are all tangent to a certain curve cc – the catacaustic of c with respect to the pole E.