Geeking out

I am a dyed-in-the-wool geek. When I first moved into my apartment here at UCI, and found out that all my stuff didn’t quite fit into my room, what did I do about it?

I drafted the floor plan of my room, and made paper cutouts of all my furniture. Then arranged and re-arranged all the paper squares until I found a layout I liked. It was a rather tedious process, but it worked quite well. The paper was much easier to shuffle around than the furniture it represented.

Then, I decided that the corner where I put my desk was not very well lit; and instead of a lamp, I wanted ceiling lights. At a nearby Lowes I saw some under-counter lights, a pack of six 20-Watt Xenon pucks. Well, given that my desk sits in a recessed section of the room, and that a line of lights isn’t nearly as nice as, say, a half-ellipse, I had to figure out some way of generating the coordinates for the placement of those lights.

Originally I was going to do this by hand, on paper, so, I checked out the wikipedia article about the ellipse; which gave me a nice parameterized formulation.

x &=& h + a \cos t \nonumber\\
y &=& k + b \sin t \nonumber
where t may be restricted to the interval -\pi \le t \le \pi.

Using this formula, I whipped up a program to generate the coordinates for the lights:

#include <QApplication>
#include <QtGui>
#include <QDebug>
int main( int argc, char *argv[] )
    QApplication app(argc, argv);
    QPixmap pix(100,100);
    QPainter painter(&pix);
    painter.setRenderHint( QPainter::Antialiasing );
    painter.setPen( QPen(QBrush(Qt::green), 1) );
    painter.drawPoint( QPointF(0.,0.) );
    painter.drawRect( -36,0, 72,24 );
    painter.setPen( QPen(QBrush(Qt::blue), 1) );
    painter.drawEllipse( -36,-24, 72,48 );
    painter.setPen( QPen(QBrush(Qt::red), 2) );
    for (int i=0; i<6; i++) {
        qreal t = 3.14159*(i+.5)/6.;
        qreal x = 36*cos(t);
        qreal y = 24*sin(t);
        qDebug() << "x: " << 36-x << " y: " << y;
    QLabel *label = new QLabel;
    return app.exec();

Which, generated the output:

x:  34.7733  y:  6.21165 
x:  25.4559  y:  16.9706 
x:  9.31752  y:  23.1822 
x:  -9.31743  y:  23.1822 
x:  -25.4558  y:  16.9706 
x:  -34.7733  y:  6.21171 
light_placement.png Lights_on_ceiling.jpg