Don  Lancaster's Guru's Lair  Math Stuff Library
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This library shelf holds tutorials and utilities on fundamental and
applied mathematics.


Included are such topics as Fourier Series, linear algebraic
equations, nonlinear graphic transforms, chain codes, digital
filters, halftone techniques, vectors and similar subjects.


Primarily by authors Don Lancaster or Jim Fitzsimons.


Note that additional math topics also appear in the Wavelets, the
Cubic Spline, and our Magic Sinewave library pages.


Most library files require an Adobe Acrobat 4.0 plug in for online
viewing.  Offline, these may be accessed by an Acrobat Reader or
an eBook Reader or any other .PDF accepting program.  

The Saga of the Dripping Stalactites STALAC.PDF #35       Celebrating the beauty of applied mathematics, first through a catalog       of our more obscure "fun with long strings of numbers" topics and       then by way of the Magic Sinewave timeline history.

Click here for the Magic Sinewave library.
Click here for a Magic Sinewave intro.
Click for a Magic Sinewave development proposal.
Click here to Order MSD-28X chips & source code.

Pixel Interpolation Algorithms PIXINTPL.PDF #83      A review of popular pixel interpolation schemes including Bilinear,      Nearest Neighbor, Bilinear with lookup, Modified 3x3, and Bicubic.      Includes detailed bicubic math derivation. .

Click here for the Pixel Interpolation utility.
Click here for the Pixel Interpolation demo..

Click here for the PostScript library.
Click here for the GuruGram 83 source code.
Click here to Contact the Author directly.


Drawing a circle through 3 points CIRC3PTS.PSL       Brief Don Lancaster tutorial and PostScript demo of drawing a      circle through three points. Finding the slope at the midpoint      leads to less tedious improved curvetracing routines.

Click here for the CIRC3PTS.PDF demo.
Click here for new CURVETR2.PSL sourcecode.
Click here fornew CURVETR2.PDF demo.


Fitting 3 points to a quadratic curve PARAFIT.PSL      Brief Don Lancaster tutorial and PostScript demo of fitting three     data points to a parabola and quickly finding the x and y values of     the minimum. For curve fitting and minimization.

Click here for Custom Research assistance.


Vector-to-step conversion tutorial VECTSTEP.PDF       Introduction and tutorial shows how to convert slanty lines into       stepper steps or screen pixels. Basic conversion. Breshenham's       method. Table lookup. Adding dimensions. Cardinal moves.

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Binomial Goes Binary ONESWORD.HTML        A PostScript utility to generate all possible binary words of length       "n" having "k" ones in them. Use for magic sinewaves & exploration.        of the binomial theorm. Requires two way recordable com.

Click here for energy efficient Magic Sinewaves.

Binary Chain Code Intro CHAIN01.HTML      A Don Lancaster tutorial and Jim Fitzsimons math program that        explores binary chain codes,. Unique self-positioning sequences.        Includes BASIC listing and chain codes for order 2 through 16.

Click here for Cubic Spline tutorials.

Tech Musings #107  MUSE107.PDF      SX laser printer repairs, linear phase digital filters, home theater        opportunities and resources , debunking some technomyths,         improved access to government surplus electronics.

Click here for more Tech Musings columns.

Tech Musings #102  MUSE102.PDF      A "colorizer" for PostScript; Using bionomial coefficients;        Laser printer repair resources; magnetic field intensity paper;        HP 5SiMX Book-on-demand printer, more.

Click here to view our Bargain Pages.

PS 4x4 Linear Equation Solver LINEQ04.PSL       Tutorial and test demo solves n=4 linear algebraic equations by      first using Gaussian Elimination followed by back substitution. This      can easily be extended to other orders.

Click here for additional Gauss-Jordan theory.

Fun With Fields FUNFIELD.PDF #39      Using PostScript to quickly solve advanced field problems      with astonishingly simple math. Gradients, Equipotentials, Laplacians.

Click here for the FUNFIELD.PSL source code.
Click here for the FIELDS01.PDF field generator.
Click here for the FIELDS01.PDF field frmo.


Click here to reach the GuruGram library.
Click here to reach the PostScript library.
Click here for additional Consulting services.
Click here to Contact the Author directly.


Tech Musings #148  MUSE148.PDF      Algae hydrogen source. Applying Taylor Series. Surplus and auction      update. Lithium polymer batteries. Understanding nonlinearity. Some      Battery books. Cave radio site, Maxim chargers, more...

Click here for Patent Avoidance info.

Tech Musings #152  MUSE152.PDF           Fundamentals of power and energy. 52 LED's from one port!         Shuffling alogrithms and pitfalls. Multi-banner auto rotator.         Thermodynamic Books. n-connectedness math.

Click here for Live Auction bargains.

Linear Equation Solver LINEAREQ.PS        A group of PostScript utilities and demos that use determinants to        solve high order linear algebraic equations. Explicit examples shown        to 10x10. Includes linear phase digital filter design examples.

Click for Auctions & Surplus library page.


Tech Musings #151 MUSE151.PDF         Radio Shack Wireless Humidity Data Format. Exergy and energy       quality. JavaScript Bouncy Buttons. Chebycheff polynomonials.         Fluxgate & magnetometry books. Plastics suppliers. More..

Click for our Pseudoscience Bashing library page.


Tech Musings #106 MUSE106.PDF       Secrets of math determinants, Power generation efficiencies, Solving       larger linear equations, induction heating fundamentals, new BOD        Book-on-demand binding opportunities.

Click here for Product Development tutorials.

Bezier curve through four points BEZ4PTS.PDF       Jim Fitzsimmons TEX tutorial shows how to fit a Bezier curve       through two end points and two intermediate points, all of which        are on the desired cubic polynomial curve.

Click for the PostScript Sourcecode utility.

Tech Musings #148 MUSE148.PDF      Algae hydrogen source. Applying Taylor Series. Surplus and auction       update. Lithium polymer batteries. Understanding nonlinearity.      Battery books. Cave radio site, Maxim chargers, more...

Click here for Custom Research assistance.


Tech Musings #105 MUSE105.PDF        H-P 5SiMx laser printer hard drive interface, new video and audio       chips, navigation resources update, understanding digital filters,       triple tri-sample building blocks, linear phase techniques.

Click here to view our Bargain Pages.

Secrets of  Nonlinear Graphics Transformations       From Circuit Cellar for August of 1995. Reviews both linear and      nonlinear transforms such as Isometric, Perspective, Tuna Can,       Star Wars, Root Beer, Spherical , Glyph Path, and Scribble.

Click here for more Circuit Cellar tutorials.

A nonlinear "Tuna Can" transform  TUNACAN.HTML       Tutorial on a quick and dirty Tuna Can transform that lets you       wrap lettering around a tilted can or cylinder. Also an example of       how to use Don's Gonzo utilities and Acrobat as PostScript interpreter.

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Hyperbolic Cubic Spline Fitting  HYSPLINE.PDF        Don Lancaster Acrobat tutorial shows the steps involved in       approximating a 1/x hyperbola with a pair of cubic splines, done        to exceptional accuracy.

Click here for more Cubic Spline info.

Tech Musings #90 MUSE90.PDF       Fourier Series analysis, alternatives to plated through holes,        classic computer resources, a $200 GPS receiver, Newtek's        new video toaster for Windows.

Click here for Fourier Series example.

PS Bezier curve through fuzzy data!  FUZZYBEZ.HTML       Don Lancaster tutorial shows how to fit a Bezier curve to fuzzy      data points. While preserving end points and optionally the exit and      entry angles. Read PS source in editor, modify , send to Distiller.

Click here for the PostScript Sourcecode.
Click here for the Acrobat PDF Demo.

Tech Musings #142 MUSE142.PDF         Contact-free battery chargers. Gage and SPS machine tool interface.         Useful energy resources. Some induction heating books.         Using Gauss Jordan Elimination to solve linear equations.

Click here for Custom Research assistance.


Hardware Hacker #83 HACK83.PDF       Halogen cycle mysteries, Science versus pseudoscience, some new       books, Vector-to-step conversion, Hacker PostScript, interconnects,        Weather satellite resources, EITD phone directory, more...

Click here for more Vector to Step tutorials.

Hardware Hacker #62 HACK62.PDF       Using cubic splines. Switchmode resources. Electrorheological       fluids. National's simple switcher. Colorized avuncular sleezoids.        Curvetracing contest. Non-ionizing radiation safety.

Click here for more Cubic Spline info.

Tech Musings #122 MUSE122.PDF       Atmel's PIC Challenger. HP's ScanJet 6100C. Finding satellite      iimagery. Understanding quadrature. Broadband phase shifters.      Using Hilbert transforms. Hydraulic rams. PostScript transparency.

Click here for Live Auction bargains.

Tech Musings #89 MUSE89.PDF       BASIC Stamp Manuals. Secrets of Fibonacci sunflowers.        New Bezier cubic spline book. Adobe's elegant Acrobat.        E-field ac voltage sensing.

Click for PostScript or Acrobat assistance.

Tech Musings #112 MUSE112.PDF         A.C. power measurement tutorial and basics. Aerogel resources         and developments. 99 cent Telephone extension lockouts.        Understanding RMS currents. Several column corrections.

Click here for more Tech Musings columns.

RMS current & voltage finder FINDRMS.PS    A PostScript utility to find the rms and average values of any complex    waveform. Especially triac phase controls. Also investigates recent     outrageous lighting efficiency claims.

Click here for Custom Research assistance.


Ken Shiriff:  VCRPlus Codes       Shows the six bit encoding and decoding of the VCRplus       time and date codes. Tutorial text, figure, and sourcecode combined       into single .PDF file from November 1993 original.

Click here for other Third Party tutorials.

Hardware Hacker #59 HACK59.PDF      High side FET drivers. Drawing semilog plots. Laser printer       repair kits. Fundamentals of resonance. Far East computing       resources. Semiconductor manufacturer resources.

Click here for more PostScript info.

Hardware Hacker #65 HACK65.PDF       Short haul telemetry and comm links. Max-Min slope theory.       SETI books and resourses. Unique new optical link. Understanding       the Maximum Power Transfer Theorem. Gerber file formats.

Click here for more Hardware Hacker columns.

Bubble Sort Utility BUBLSORT.PS        Simple stack-oriented utility that bubble sorts up to several        thousand values. Read tutorial first as textfile, then test and        modify as runnable PostScript code.

Click here for additional PostScript resources.

Insertion Sort Utility INSORT.PS       Simple stack-oriented utility that approximates an insertion sort       up to several thousand values. Read tutorial first as textfile, then       test and modify as runnable PostScript code.

Click here for Adobe Acrobat PDF info.

Resources from Math Net        This appears to be the defining site for all links mathematical       currently on the web.

Click here for the Hotbot search engine.
Click here for the Google search engine.

Click here for Cubic Spline tutorials.
Click here for Custom Consulting assistance.
Click here for Magic Sinewave tutorials.
Click here for some Wavelet tutorials.

Bezier Curves & Cubic Splines:

B-Spline Knot Insertion and Deletion Algorithms ( Roger Goldman ) Curves and Surfaces  ( Academic Press ) Curve and Surface Fitting  ( Peter Lancaster ) An Introduction to Nurbs  ( David Rodgers ) Geometric Modeling using Beta Splines  ( Brian Barsky ) Handbook of Splines  ( Gheorghe Micula ) Handbook of Splines for the User  ( Eugene Shikin ) Interpolating Cubic Splines  ( Gary Knott ) Methods of Shape; Preserving Spline Approximation ( Boris Kvasov ) The Nurbs Book  ( Les Piegelr ) Nurbs for Curves and Surface Design  ( Gerald Farin ) PostScript Language Reference Manual   ( Adobe Systems ) A Practical Guide to Splines ( Carl De Booer ) Spline Functions ( K. Bohmer ) Theory of Splines and Applications  ( J. Ahlberg ) Two Dimensional Spline Interpolation Algorithms  ( Helmuth Spath )

Error Correcting Codes:

Principles of Digital Communication ( Andrew Viterbi)   1997 Error Correcting Code Symposium (Harold Mattson) Algebraic Algorithims and Error-Correcting... (John Alton) Applicable Algebra, Error-Correcting Codes, ... (Beth Th) CDMA; Principles of Spread Spectrum Comm (Andrew Viterbi) Coded Modulation for Fading Channels (Hamidreza Jamali) Data & Computer Communications (William Stallings) Engineer's Error Coding Handbook (A Houghton) Error Control Coding (Shu Lin) Error Control Systems for Digital Comm... (Stephen Wicker) Error Control Techniques for Digital Comm... (Arnold Michelson) Error Correcting Codes (John Baylis) First Course in Coding Theory (Raymond Hill) Introduction to Error-Correcting Codes (Michael Purser) Intro to Error Correcting Codes (Scott Vanstone) Theory & Applications of Error-Correction Codes (Jiri Adamek) Trellis Coding  (Christian Schlegel) Voice & Data Communications Handbook (Regis Bates) Understanding Data Communications (Gilbert Held)

Wavelets:

An Introduction to Wavelets ( Charles Chui ) Applied Wavelet Analysis with S-Plus ( Andrew Bruce ) Fourier and Wavelet Analysis  ( George Bachman ) Fractal and Wavelet Image Compression Technique  ( Stephen. Welstead ) Handbook of Wavelet Transform Algorithms ( Carl Taswell ) Introduction to Wavelet Transforms ( Ramesh Gopinath ) Multirate and Wavelet Signal Processing  ( Bruce Suter ) Multiscale Wavelet Methods for PDE ( Wolfgang Dahmen ) Signal and Image Representation in Combined... ( Y. Zeev ) Signal Processing With Wavelet-Based Fractals ( G. Wornell ) Wavelet Analysis for Image Processing ( L. Prasad ) Wavelet Analysis: Scalable Info Structure ( H. Resnikoff) Wavelet Basics (Y. Chan ) Wavelet Theory and Pattern Recognition ( Yuan Y. Tan ) A Wavelet Tour of Signal Processing ( Stephane Mallat ) Wavelet Transforms & Applications ( Mysore Raghuveer ) Wavelets: A Tutorial in Theory & Applications ( Charles Chui ) Wavelets: Theory, Algorithms & Applications ( C. Chui )

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