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

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

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

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

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

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

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

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

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

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

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.

#### Flight Simulator Tutorial #4 – matrix allocation and input parameter formulas (roll rate, pitch rate, throttle)

This section explains the top level functionality of the model, it also allocates the data and formula arrays needed for manipulating the scene image. The roll rate, pitch rate and throttle formulas are implemented in the worksheet.

#### A First Flight Simulator Model in Excel

This is the first version of a 3D flight simulator in Excel. Start by adjusting the zoom on your file to fit the screen, so you can see the whole chart and the buttons underneath, then click “Reset” and then click the red dot in the center of the joystick. After that, the joystick handle will “stick” to your mouse pointer so your mouse becomes the airplane control. Back and forth mouse…

#### A Legacy 3D Octal Planetary Model

This is an older model of planetary motion in 3D containing eight planets. A video preview can be watched here.

#### Flight Simulator Tutorial #3 – scene rotations and translation

This section deals with a simple method of creating the appearance of scene movement during the flight. Beside reviewing standandard rotation and translation formulas described before on this blog, the presentation begins to explain how to apply numerical-like methods to create a live and interactive model.

#### MDETERM() & MINVERSE() – two important Excel spreadsheet functions for matrix manipulations

This is a brief tutorial showing how to calculate the determinant of a matrix and the inverse of a matrix using two special spreadsheet functions MDETERM() and MINVERSE().

#### Flight Simulator Tutorial #2 – basic airplane positioning, control surfaces and turn dynamics

This is the second part of a tutorial explaining the creation of an “in-cockpit” flight simulator (versus the remote control simulator) model in Excel 2003. This section introduces some basic piloting background and nomenclature.

#### TRANSPOSE() & MMULT() – two important Excel spreadsheet functions for matrix manipulations

This is a tutorial introducing two important matrix manipulation spreadsheet functions in Excel: the matrix transposition function TRANSPOSE() and the matrix multiplication function MMULT(). These functions are a bit harder to use than the regular spreadsheet functions in the sense that the result is a matrix and a matrix cell range is treated by the program as a unity (you cannot change the formula since you cannot operate on a single cell). There are some…

#### Flight Simulator Tutorial #1 – the joystick and a ground mesh

This is the first section of a tutorial explaining how to build a 3D flight simulator in Excel. This part deals with creating a joystick and a triangular ground mesh. The joystick model was explained in a previous post from January 2011 and the ground mesh was already used in the 3D roller-coaster. Please be aware that both the PDF and Excel files for this section have been updated on 4/13/2011 at 7:15 pm.

#### Spectral Analysis – a Fourier transform tutorial – part #5

This part of the tutorial demonstrates the Fourier transform operation in a few cases of periodic and aperiodic signals, such as an AM signal, an FM signal, a rectangular nonrepetitive signal and a cardinal sinus signal. The last slide contains an application to the scaling property of the Fourier transform on a nonrepetitive time signal. It actually shows that spreading a signal in the time domain shrinks its spectrum and…

#### Spectral Analysis – a Fourier transform tutorial – part #4

The previous sections explaind the creation of a discrete Fourier transform model in Excel. This section and the following one will use the model to calculate and chart the Fourier transform in several cases of periodic and aperiodic signals.