CAD Test Work, Subtract the Kinematic Solid from the Parallelepiped

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Task

A 3d Euclidian point cloud aligned in main axis directions (x, y, z) and with a constant distance grid (Figure 1) starting at a given reference point (the point with indices 0, 0, 0 is located at reference point) is intersected by a move of sphere (Figure 2), where the path of the sphere center is defined by a user given formula x = f(t) where t is in the interval between t0 and t1. The function f(t) can be handled as a discrete function with a user given ∆t. Points that intersect with the sphere move are considered as deleted (Figure 3 middle).

Only the first layer of points (which remains visible/undeleted) from top view must be written to a file as ASCII data (the skin of the point cloud from top view, see Figure 3 right). The file format is defined as follows:

• Each line contains a single point.
• The point definition contains x, y and z coordinates delimited by space characters.
• Each line ends with a new line character.

Illustrations

Given

• Point class for the definition of a point in 3d and (some) methods for vector algebra.
• High level test function CreateSkin(. . .) (in src/CreateSkin.cpp) to test the resulting component. This defines also the interface of the component to be written.
• Program named 'PointVisualizer' (see tools/PointVisualizer_* files) which allows you to view the results you obtain in 3d.

Hints

• Use of vector algebra (dot product, cross product etc.) is highly recommended. The use of sin and cos functions is not desired.
• Calculation speed and memory footprint are important but secondary in comparison to clearly readable code. E.g. a sphere, linear move of a sphere, point writer etc. might be modeled as classes. Prefer compact classes and functions over large classes and functions.
• Comments in the source code are welcome. Please use good names for classes and functions.
• Move of a sphere between f(t) and f(t + ∆t) can be assumed as a linear move of the center of the sphere.

Solution

Regarding this task, a given point cloud can be considered as a certain geometric solid bounded by a parallelepiped of dimension nX x nY x nZ, located in space with a given reference point referencePoint and filled with points of a given crystal lattice.

When moving a given sphere along an arbitrary user-defined function f(t), we obtain a solid of the motion, or a kinematic solid.

Next, need to perform a Boolean operation of subtraction of the obtained kinematic solid K from the initial parallelepiped P. As a result, we get a new solid P` = P − K.

And then need to leave only the uppermost points from the resulting solid P`, which have the largest value of the coordinates along the Z axis.

Used Books

• Голованов Н. Н. Геометрическое моделирование. — М.: Издательство Физико-математической литературы, 2002. (Golovanov N.N. Geometric modeling. — Moscow: Publisher of physical and mathematical literature, 2002.)

Code

Solution code with using the C++ and the vector algebra is presented in the src/TaskSolution.hpp and src/TaskSolution.cpp files.

CMake is used to build the project, for this reason the CMakeLists.txt file was created.

Build

Make the following commands to build the project:

mkdir ./build
cd ./build
cmake ..
cmake --build .