#### A Preliminary 2D Ray Tracing Demo for Spherical Mirrors in Excel

30/04/2011

This is a demonstrative model for 2D spherical mirror ray tracing in Excel. It works in Excel 2003 at about 40 frames per second and in Excel 2007 at about 4 frames per second. You can start it in  a hands-off demo mode by clicking the “Fully Automatic Demo” button and at any time you can hit the the “Demo Style” button to choose a flexible (pulsating) mirror or a…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 4

29/04/2011

This section begins by charting the incident rays on the same 2D acatter chart with the mirror and then explains how to derive the Cartesian coordinates for a “final” point which together with the point of incidence will define the reflected ray. A custom VBA function is created for this purpose.

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 3

28/04/2011

This section explains explains how to implement the formulas that define the emergent (reflected) rays into a custom VBA function. Though geometrically the last two presentation might look a little  elaborate, just be patient and follow the presentation, or even better try to just sneak peek and do it yourself. All this derivation is done based on first principles and some Mickey Mouse geometry. Take all the time you need, a day, a week…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 2

27/04/2011

This section explains the illumination setup by using an artificial star, derives the equations of the incident rays and also solves the system of equations for finding the exact coordinates of the points where the incident rays hit the mirror. Looking at the sign of the determinant of a quadratic equation involved in finding the intersection between an incoming ray and the mirror we can say if the ray hits…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 1

26/04/2011

This is a first post of an introduction to optics series and it explain how to create a 2D ray tracing model for a spherical mirror. This section deals with the creation and charting of the mirror using a parametric equation for a circle. This post has been updated on 4/28/2011 at 7pm GMT.

#### A Solver for Systems of Linear Equations in Excel

25/04/2011

This is a linear system of equations solver in Excel. The size of the system is programmable by the user from 2 to 20 which means, depending on the setting selection, the model can instantly find the solution of linear systems starting from 2 equations and 2 unknowns up to 20 equations and 20 unknowns. It uses the following built-in Excel spreadsheet functions: MMULT(), MINVERSE() and TRANSPOSE(). Like everything on…

#### The Easy Way of Solving Systems of Linear Equations in Excel – using the INVERSE() spreadsheet function

24/04/2011

This brief tutorial explains how to calculate the solution vector of a system of linear equations using the Excel spreadsheet function MINVERSE() which calculate the inverse of a matrix.

#### Flight Simulator Tutorial #7 – upgrading the joystick chart, adding a reset button and a throttle scroll bar

22/04/2011

This section displays the landscape on a 2D scatter chart and also upgrades the joystick chart by adding a dial behind the joystick image. This technique of using a stack of a back chart to display dial sprites and a front chart with transparent background to display various control devices, indicator needles and text will extensivly be used in this and future models.

#### Flight Simulator Tutorial #6 – macro review, scene derivation and integration, mapping of the 2D u-v data into a chartable 1D array, rejecting image artifacts

21/04/2011

This section finishes the macro analysis and continues with the conversion of the u-v 2D formula array into a chartable 1D array. It also adds two columns to the chartable array, a masking condition for each triangle and masked u-coordinate which will throw out of the visible portion of the chart any shape which has a minimum of one vertex behind the virtual pilot. The section also explains the phenomenon…

#### Flight Simulator Tutorial #5 – the worksheet implementation of the perspective handling formulas and VBA the macros

20/04/2011

This section explains the spreadsheet  implementation of the perspective rotation and translation formulas within the Present array and also the implementation of the 3D-2D conversion formulas within the Past array, then it goes on to presenting the VBA macros used (the Reset and JoyStick macros). The PDF and XLF files were updated -04/22/2011, 5:20 pm MST.