Delphi Graphics
Delphi
Graphics
Image Processing
Mathematics

// Given points(iText,jText) and (iTarget,jTarget). The angle between
// the x-axis and the vector (iTarget-iText, jTarget-jText) ranges in the
// open interval [0.0, 360.0) degrees.  (0 degrees is the +X axis).
//  Note: Normally, ArcTan2 returns a value from -PI to PI.
angle := 180 * (1 + ArcTan2(jText-jTarget, iTarget-iText) / PI);
IF    angle >= 360.0
THEN angle := angle - 360.0;

Clock Angles
www.delphiforfun.com/Programs/clock_angle.htm 

The TCanvas.Arc method is is not that easy to use for some applications.  The DrawArcs demo shows how to define a bounding rectangle and then draw the specified type of arc between opposite corners of the rectangle.

TYPE
  TArcOrientation = (aoSouthWest, aoSouthEast, aoNorthEast, aoNorthWest);

BoundRect := Rect(xMin,yMin, xMax,yMax);

DrawArc(Bitmap.Canvas, clLime,  aoSouthWest, xMin,yMin,xMax,yMax, BoundRect); 
DrawArc(Bitmap.Canvas, clBlack, aoSouthEast, xMin,yMax,xMax,yMin, BoundRect);
DrawArc(Bitmap.Canvas, clBlue,  aoNorthEast, xMax,yMax,xMin,yMin, BoundRect);
DrawArc(Bitmap.Canvas, clRed ,  aoNorthWest, xMax,yMin,xMin,yMax, BoundRect);

Paul Nicholls' UseNet Post about how to compute polygon area using 3D points
Clive Tooth's UseNet Post about Area of Spherical Triangle

TriangleArea and TriangleHeight functions in William Egge's EMath unit

See efg's  MapWorldToPixel unit for a quick way to map (x,y) to (i,j).

Dave Shapiro's UseNet Post explaining "Why is 'y' upside down?" (or how to make the y-axis increase from bottom-to-top instead of top-to-bottom)

See GraphicsMath (below) for Pantograph objects that perform this mapping for 2D/3D vectors, along with projections and clipping.

"Windows 95/98 uses a 16-bit world coordinate system and restricts x- and y- coordinates for text and graphics to the range ±32K. Windows NT/Windows 2000 uses a 32-bit world coordinate system and allows coordinates in the range ±2 gigabytes (GB). If you pass full 32-bit coordinates to text and graphics functions in Windows 95/98, the system truncates the upper 16 bits of the coordinates before carrying out the requested operation."

"Because Windows 95/98 uses a 16-bit coordinate system, the sum of the coordinates of the bounding rectangle specified by the Arc, Chord, Pie, Ellipse, and RoundRect functions cannot exceed 32K. In addition, the sum of the nLeftRect and nRightRect parameters or the nTopRect and nBottomRect parameters cannot exceed 32K.""

[Of course Microsoft broke the link with this information so the original MSDN reference in no longer available.]

Jean-Yves Queinec's Bézier project

Béziers and Paths by Clinton R. Johnson
www.undu.com/Articles/980326b.htm

Alexander Weidauer's UseNet Post showing a  "function to draw a Bézier curve starting from a variable
number of points"

Drawing Curves
www.gnomehome.demon.nl/uddf/pages/graphics.htm#graphics1

The "Bezier Draw" is a sample Delphi program to demonstrate the use of "Bezier" unit.
www.programmersheaven.com/zone2/cat262/16261.htm 

See PolyBezier API call

efg's D7 project to create this mathematical butterfly

Division of Semicircle into 2^N Intervals Using Half-Angle Formula and Rotation Formula
efg's Buffon Lab Report

See "Circle Approximation" as part of Polygon Area and Centroid Lab Report

efg's UseNet Post about computing great circle distances

MUMIL - a cursor based contouring routine
www.triplexware.huckfinn.de/contweber.html 

Distance from point P1(x1, y1) to Line, a*x + b*y + c = 0
ABS( a*x1 + b*y1 + c ) / SQRT( SQR(a) + SQR(b) )

DistPoint2Line and DistPoint2LineSegment functions in William Egge's EMath unit

Using a background thread to compute and display a Mandelbrot set using HSVcolor scheme, Delphi in a Nutshell, pp. 148-151

Borland's Fractal Generator Contest
http://homepages.borland.com/ccalvert/Contest/MarchContest/Announce.html

Chapter 6, "3D Fractal Landscapes" in Kick Ass Delphi Programming (out of print)
www.midnightbeach.com/jon/pubs/3D_Fractal_Landscapes.html 

Geometry Library, Geometry.ZIP.  This unit contains types, functions and procedures for quaternion, vector and matrix arithmetics. It is specifically designed for geometric calculations within R3 ("affine" vector space) and R4 (homogeneous vector space).
www.lischke-online.de/Graphics.php 

efg's GraphicsPrimitivesLibrary unit (uses GraphicsMathLibrary unit) defines a TPantoGraph class.  A TPantoGraph object maps 2D/3D "World Coordinates" to a Delphi "Canvas".  These World Coordinates are DOUBLE values that are defined using regular mathematical conventions. This means that instead of having  increasing "Y" values as you go down a canvas, "Y" increases as you go up using the computer "pantograph".   Includes clipping and various projection options.

Suggestion by CC.Campbell for using TextOut with TPantograph

Read TXT file into dynamically allocated matrix and show matrix as either gray scale or "rainbow" values:

10 8
 0.000 -0.321 -0.285  0.267  1.344  2.656  3.733  4.285  4.321 4.000
 0.355  0.062 -0.073  0.150  0.904  1.953  2.707  2.930  2.795 2.502
 0.039  0.014 -0.012  0.050  0.468  1.246  1.664  1.727  1.700 1.675
-1.166 -0.854 -0.547 -0.250  0.048  0.524  0.821  1.119  1.426 1.737
-2.834 -2.257 -1.675 -1.084 -0.492 -0.079  0.512  1.103  1.685 2.263
-4.039 -3.125 -2.210 -1.383 -0.913 -0.801 -0.331  0.496  1.411 2.325
-4.355 -3.173 -2.149 -1.483 -1.348 -1.509 -1.374 -0.708  0.316 1.498
-4.000 -2.790 -1.937 -1.600 -1.789 -2.211 -2.400 -2.063 -1.210 0.000

(A "LargeMatrix" program is included to create large test matrices.  A 1200-by-900 matrix will take about 5 minutes on a 650 MHz Pentium III.)

adub's UseNet Post with PtInPolygon using PtInRegion WinAPI call

PointAndPolygon unit with PointInPolygon function by Philippe De Boe and Thérèse Hanquet

Paul Nicholls' UseNet Post with point-in-polygon routine

John Hutchings' UseNet Post with PointInPolygonTest function

// InSide function by Andreas Filsinger
function InSide (const x,y : integer; Polygon: array of TPoint): boolean;
  var
     PolyHandle: HRGN;
begin
   PolyHandle := CreatePolygonRgn(Polygon[0],length(Polygon),Winding);
   result     := PtInRegion(PolyHandle,X,Y);
   DeleteObject(PolyHandle);
end;

Geir Wikran's UseNet Post with PointInPolygon function
Joe Hecht's UseNet Post with three suggested methods

Also see PtInRegion on Graphical Win32 API page

efg's Maxwell Triangle Lab Report

efg's Line Stretch Lab Report with NearLine function

BSplines.ZIP by Martijn an Engeland. Component for handling and displaying BSplines. Delphi Super Page: http://delphi.icm.edu.pl/ftp/d10free/bsplines.zip

[Foley96, pp. 1013-1018]

The "Twirl" program is based on the spiral transform from Beyond Photography:   The Digital Darkroom (the book is online) by Gerard J. Holzmann, Prentice-Hall, 1988, pp. 44-45.  The book gives the formula for transforming a picture of Ken Thompson (one of the originators of UNIX):

new[radius, angle] = ken[radius, angle + radius/3]

Twist.ZIP (D3-D5 complete project with source code -- BMPs not included)