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Thanks for the help. I didn't know because, like, Euclid retired before I even started school. -
It's absolutely simple.Originally posted by Michael Mattias View Post
You look at the thing, and you say to yourself that there must be a fixed relationship between two aspects.
Then you look for that relationship. Eventually, you are able to obtain enough data from observations.
Then you are able to construct a formal expression of the relationship, which you then test.
I can get the first part. The rest is Greek.
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Euclid din't know about sines etc. You are confusing trigonomentry with geometry (the axioms of which Euclid did develop). SInes etc didn't come into use until the Indian and Arabic mathematicians derived the concepts many centuries later.Originally posted by Michael Mattias View Post
It's a long story. Early trigonometry came a few centuries after Euclid and started with the chord - the arc subtended by an angle and the ratio of the chord to the radius. That one is easly to derive since 1° is 1/360th of the circumference. It is what thet Greeks such as Ptolemy used for astronomical claculations.Leave a comment:
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No, no, before that. Like, how the heck did Euclid get them?At a guess, I'd say "trig tables" come from Trigonometry
Computers generall calculate them, using the CORDIC algorithm.Leave a comment:
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the below codes with some graphics inclusive of X and Y axes, please comment on it and enhance it
so that a better program emerges. Noteworthy I have pirated some codes from Stuart and Dave Biggs as well as improving it with Dan Soper's suggestion. Thanks everyone on this
There are 10 data sets to test these codes and please uncomment each set to test it as well
as displaying its graphics
Code:' Point on Line.bas ' https://forum.powerbasic.com/forum/user-to-user-discussions/programming/816417-need-codes-to-find-equation-of-straight-line-y-mx-b?p=816429#post816429 ' Obtain the equation of a line given 2 points (x1,y1) and (x2,y2) ' check whether point (x3,y3) lies on this line ' Great Thanks to Stuart , Dave Biggs #COMPILE EXE #DIM ALL FUNCTION PBMAIN() AS LONG LOCAL x1,x2,x3,y1,y2,y3,gradM,IntC AS DOUBLE LOCAL wstrF, wstrL , wstrBet AS WSTRING LOCAL FlagbetX , FlagbetY AS LONG LOCAL setNumSt AS STRING 'Set 1 -- y = 2x where test point is on the line and lies between ' the line points 'Line points ' x2 = 1 : y2 = 2 ' x1 = 4 : y1 = 8 'Test point ' x3 = 3 : y3 = 6 ' setNumSt = " 1" 'Set 2 -- answer check correct y = -3x -5 test point is NOT on line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x1 = -5 : y1 = 10 ' x2 = -3 : y2 = 4 'Test point ' x3 = -2 : y3 = 7 ' setNumSt = " 2" 'Set 3 -- answer check correct y = 6x +4 test point is on line but not between line points ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = -5 : y2 = -26 'x1 = -2 : y1 = -8 'Test point ' x3 = -7 : y3 = -38 ' setNumSt = " 3" 'Set 4 -- answer check correct y = 6x +4 test point is on line and lies between ' the line points ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = -5 : y2 = -26 ' x1 = -2 : y1 = -8 'Test point ' x3 = -3 : y3 = -14 ' setNumSt = " 4" 'Set 5 -- answer check correct y = 4.5x - 24 test point is NOT on the line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = 6 : y2 = 3 ' x1 = 4 : y1 = -6 'Test point ' x3 = 3.6 : y3 = -10 ' setNumSt = " 5" 'Set 6 -- answer check correct y = 1.5x - 2.5 test point is NOT on the line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = 3 : y2 = 2 ' x1 = 5 : y1 = 5 'Test point ' x3 = 4 : y3 = 4 ' setNumSt = " 6" ' Set 7 -- horizontal line y = 2 'Line points ' x2 = 3 : y2 = 2 ' x1 = 5 : y1 = 2 'Test point ' x3 = 4 : y3 = 3 ' setNumSt = " 7" ' Set 7B -- horizontal line y = 2 'Line points ' x2 = 3 : y2 = 2 ' x1 = 5 : y1 = 2 'Test point ' x3 = 4 : y3 = 2 ' setNumSt = " 7B" 'Set 8 -- Vertical line X = 2 'Line points 'x2 = 2 : y2 = 3 ' x1 = 2 : y1 = -6 'Test point ' x3 = 2 : y3 = 3 ' setNumSt = " 8" 'Set 8B -- Vertical line X = 2 'Line points x2 = 2 : y2 = 3 x1 = 2 : y1 = -6 'Test point x3 = 1.5 : y3 = -1.8 setNumSt = " 8B" ' check that all coordinates are valid IF x1 = 0 AND y1 = 0 THEN IF x2 = 0 AND y2 = 0 THEN ' all coord are Invalid ? " invalid coordinates " EXIT FUNCTION END IF END IF IF x1 = x2 AND y1 = y2 THEN ' all coord are Invalid ? " invalid coordinates " EXIT FUNCTION END IF wstrF = "The equation for the line" & $LF & _ "(" & STR$(x1,4) & " , " & STR$(y1,4) & ") - (" & _ STR$(x2,4) & " , " & STR$(y2,4) & ") is :" & $LF wstrL = $LF & $LF & "The point (" & STR$(x3,4) & " ," & STR$(y3,4) & ") " LOCAL smallNum AS DOUBLE smallNum = 0.0001 IF x1 = x2 THEN 'line is vertical wstrF &= "X = " & STR$(x1,3) IF x3 = x1 THEN 'point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE wstrF &= "Y=" IF y1 = y2 THEN ' line is horizontal wstrF &= STR$(y1,4) IF y3 = y1 THEN ' point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE ' line is neither horizontal nor vertical gradM = (y2-y1)/(x2-x1) IntC = (x2*y1-x1*y2)/(x2-x1) IF ABS(gradM)= 0 THEN wstrF &= STR$(IntC,3) ELSE wstrF &= STR$(gradM,4) & "X " & IIF$(IntC>=0," +"," ") & STR$(IntC,3) END IF ' Thanks to Dan to use a smallNum check ' https://forum.powerbasic.com/forum/user-to-user-discussions/programming/816417-need-codes-to-find-equation-of-straight-line-y-mx-b?p=816444#post816444 IF ABS(y3 - (gradM*x3 + IntC)) <= smallNum THEN wstrL &= " is on the line" ' check if x3 is between x1 and x2 FlagbetX = 0 IF x2 >= x1 THEN IF x3 >= x1 THEN IF x3 <= x2 THEN FlagbetX = 1 END IF END IF ELSE IF x3 >= x2 THEN IF x3 <= x1 THEN FlagbetX = 1 END IF END IF END IF ' check if y3 is between y1 and y2 FlagbetY = 0 IF y2 >= y1 THEN IF y3 >= y1 THEN IF y3 <= y2 THEN FlagbetY = 1 END IF END IF ELSE IF y3 >= y2 THEN IF y3 <= y1 THEN FlagbetY = 1 END IF END IF END IF wstrBet = $CRLF +"But it does NOT lies between the given Line points" IF FlagbetX + FlagbetY = 2 THEN wstrBet = $CRLF + "And it also lies between the given Line points" END IF ELSE wstrl &= " is NOT on the line" END IF END IF END IF ' draw the graphics ' pirated from ' https://forum.powerbasic.com/forum/user-to-user-discussions/powerbasic-for-windows/816259-how-to-draw-a-polygon-graphically?p=816366#post816366 LOCAL hGraph AS DWORD LOCAL xmin,xmax ,ymin, ymax AS DOUBLE LOCAL xmark, ymark AS DOUBLE ' marks per axis LOCAL NumStep AS LONG ' canvas margins LOCAL lm, tm, rm, bm AS DOUBLE ' scaled margins LOCAL slm, stm, srm, sbm AS DOUBLE ' scaled xy coordinates for circular dots LOCAL scx , scy , xrat , yrat AS DOUBLE LOCAL TitleLab, XaxisLab, YaxisLab AS STRING LOCAL hFont1, hFontR AS DWORD ' set up fonts FONT NEW "Lucida Console", 10, 0, 0, 0, 0 TO hFont1 ' rotated font (needs to be true type) FONT NEW "Lucida Console", 10, 0, 0, 0, 900 TO hFontR ' obtain the min and max coord of the 3 points ' to do the scaling xmin = MIN(x1,x2,x3) ymin = MIN(y1,y2,y3) xmax = MAX(x1,x2,x3) ymax = MAX(y1,y2,y3) GRAPHIC WINDOW NEW "Line and points",100,100,500,500 TO hGraph GRAPHIC ATTACH hGraph, 0 'white background GRAPHIC CLEAR %WHITE ' Left , Right, Top and Bottom Canvas Margins (in pixels) ' adjust these to the canvas window size ' lm = 80 : rm = 60 : tm = 70 : bm = 90 lm = 130 : rm = 60 : tm = 90 : bm = 140 ' Calculate the scaled margins slm = lm * (xmax-xmin)/(GRAPHIC(CANVAS.X) - lm - rm) srm = rm * (xmax-xmin)/(GRAPHIC(CANVAS.X) - lm - rm) stm = tm * (ymax-ymin)/(GRAPHIC(CANVAS.Y) - tm - bm) sbm = bm * (ymax-ymin)/(GRAPHIC(CANVAS.Y) - tm - bm) ' adjustments if scaled margins are zero IF slm = 0 THEN slm = lm * (xmax -xmax*0.5)/(GRAPHIC(CANVAS.X) - lm - rm) END IF IF srm = 0 THEN srm = rm * (xmax-xmax*0.5)/(GRAPHIC(CANVAS.X) - lm - rm) END IF IF stm = 0 THEN stm = tm * (ymax-ymax*0.5)/(GRAPHIC(CANVAS.Y) - tm - bm) END IF IF sbm = 0 THEN sbm = bm * (ymax-ymax*0.5)/(GRAPHIC(CANVAS.Y) - tm - bm) END IF ' ? STR$(slm) + " " + STR$(srm) + " " + STR$(stm) + " " + STR$(sbm) ' x , y ratios of canvas xrat = (xmax-xmin)/GRAPHIC(CANVAS.X) yrat = (ymax-ymin)/GRAPHIC(CANVAS.Y) IF xrat = 0 THEN xrat = (xmax-xmax*0.5)/GRAPHIC(CANVAS.X) END IF IF yrat = 0 THEN yrat = (ymax-ymax*0.5)/GRAPHIC(CANVAS.Y) END IF ' calculate the size of the circular dot for the points ' adjust the multiplier to suit size of dot scx = 7 * xrat scy = 7 * yrat ' Scale Windows so that points coordinates fit nicely GRAPHIC SCALE (xmin-slm, ymax+stm) - (xmax+srm, ymin-sbm) ' Line is in Lime over a white background GRAPHIC WIDTH 1 GRAPHIC COLOR %RGB_LIME, %WHITE ' Draw the line GRAPHIC LINE (x1,y1) - (x2,y2) ' draw the points in large dots GRAPHIC BOX (x1-scx,y1-scy) - _ (x1+scx, y1+scy),100,%RGB_BLUE,%RGB_BLUE GRAPHIC BOX (x2-scx,y2-scy) - _ (x2+scx, y2+scy),100,%RGB_BLUE,%RGB_BLUE ' the third point in Magenta GRAPHIC BOX (x3-scx, y3-scy) - _ (x3+scx, y3+scy),100,%RGB_MAGENTA,%RGB_MAGENTA ' draw the axes ------------------------------------------------------- ' calculate axes mark spacing based on data range / values NumStep = 10 IF xmax = xmin THEN xmark = CalculateStepSize(xmax*0.5, xmax, NumStep) ELSE xmark = CalculateStepSize(xmin, xmax, NumStep) END IF IF ymax = ymin THEN ymark = CalculateStepSize( ymax*0.5, ymax, NumStep) ELSE ymark = CalculateStepSize(ymin, ymax, NumStep) END IF ' Draw the axes labels GRAPHIC COLOR %RGB_MEDIUMBLUE, %WHITE TitleLab = "Plot for data set #" + setNumSt GRAPHIC SET FONT hFont1 GRAPHIC SET POS (xmax-(xmax-xmin)/2 - _ GRAPHIC(TEXT.SIZE.X, TitleLab)/2, ymax + stm*0.4) GRAPHIC PRINT TitleLab ' Display the x axis label XaxisLab = "X-Axis" GRAPHIC SET POS (xmax-(xmax-xmin)/2 - _ GRAPHIC(TEXT.SIZE.X, XaxisLab)/2, ymin - sbm*0.45) GRAPHIC PRINT XaxisLab ' Draws the x axis line GRAPHIC WIDTH 2 GRAPHIC COLOR %RGB_BLACK, %WHITE GRAPHIC LINE (xmin, ymin) - (xmax, ymin) GRAPHIC WIDTH 1 ' draw marks on the x axis LOCAL nchar AS LONG LOCAL rr AS DOUBLE LOCAL km AS LONG km = 0 FOR rr = xmin TO xmax STEP xmark INCR km GRAPHIC LINE (rr, ymin) - (rr, ymin-GRAPHIC(CELL.SIZE.Y)*0.75) ' Display the mark values nchar =LEN( TRIM$(STR$(rr),ANY CHR$(0) + CHR$(32)+ CHR$(10) + CHR$(13)+ CHR$(9))) IF nchar = 1 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*0.55, - GRAPHIC(CELL.SIZE.Y)*0.5) ELSEIF nchar = 2 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*0.9, - GRAPHIC(CELL.SIZE.Y)*0.5) ELSEIF nchar = 3 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*1.5, - GRAPHIC(CELL.SIZE.Y)*0.5) ELSE GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*1.8, - GRAPHIC(CELL.SIZE.Y)*0.5) END IF ' print the scale values on x axis ' (alternate values only to prevent clutter) IF km MOD 2 = 0 THEN IF xmark < .1 THEN GRAPHIC PRINT TRIM$(FORMAT$(rr, "0.00")) ELSEIF xmark < 1 THEN GRAPHIC PRINT TRIM$(FORMAT$(rr, "0.0")) ELSE GRAPHIC PRINT TRIM$(rr) END IF END IF NEXT rr ' Display the y axis label ' Using rotated font at 90deg YaxisLab = "Y-Axis" GRAPHIC SET FONT hFontR GRAPHIC SET POS (xmin-slm*.7, (ymax-(ymax-ymin)/2) _ - GRAPHIC(TEXT.SIZE.X, YaxisLab)/2) GRAPHIC PRINT YaxisLab ' back to font1 GRAPHIC SET FONT hFont1 ' Draw the y axis line GRAPHIC WIDTH 2 GRAPHIC COLOR %RGB_BLACK, %WHITE GRAPHIC LINE (xmin, ymin) - (xmin, ymax) GRAPHIC WIDTH 1 ' draw marks on the Y axis LOCAL tmpSt AS STRING km = 0 FOR rr = ymin TO ymax STEP ymark INCR km GRAPHIC LINE (xmin, rr) - (xmin-GRAPHIC(CELL.SIZE.X), rr) ' Display the mark values IF rr < .1 THEN tmpSt = TRIM$(FORMAT$(rr, "0.00")) ELSEIF rr < 1 THEN tmpSt = TRIM$(FORMAT$(rr, "0.0")) ELSEIF rr = 0 THEN tmpSt = TRIM$(STR$(rr)) ELSE tmpSt = TRIM$(STR$(rr)) END IF nchar =LEN(TRIM$(tmpSt,ANY CHR$(0) + CHR$(32)+ CHR$(10) + CHR$(13)+ CHR$(9))) IF rr = 0 THEN nchar = 1 END IF IF nchar <= 2 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*3, GRAPHIC(CELL.SIZE.Y)/2) ELSEIF nchar = 3 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*4.2, GRAPHIC(CELL.SIZE.Y)/2) ELSEIF nchar >= 4 THEN GRAPHIC SET POS STEP (-GRAPHIC(CELL.SIZE.X)*4.5, GRAPHIC(CELL.SIZE.Y)/2) END IF ' print scale values -- alternate values only ' to prevent cluther IF km MOD 2 = 0 THEN IF ymark < .1 THEN GRAPHIC PRINT TRIM$(FORMAT$(rr, "0.00")) ELSEIF ymark < 1 THEN GRAPHIC PRINT TRIM$(FORMAT$(rr, "0.0")) ELSE GRAPHIC PRINT TRIM$(rr) END IF END IF NEXT rr ' display the messagebox ? wstrF & wstrL & wstrBet GRAPHIC WAITKEY$ GRAPHIC WINDOW END hGraph END FUNCTION ' Thanks to Dave Biggs ' Compute the marks positions on the axes ' Approximately there are around 10 marks on each axes FUNCTION CalculateStepSize(dmin AS DOUBLE, dmax AS DOUBLE, NStep AS LONG) AS DOUBLE LOCAL dRange, tempstep, StepSize AS DOUBLE LOCAL mag, magPow, magMsd, mult AS LONG ' NStep = 10 ' eg maximum marks on axis dRange = dmax -dmin IF dRange = 0 THEN EXIT FUNCTION END IF ' calculate an initial guess at step size tempStep = dRange/NStep ' scale up low magnitude step sizes (avoid negative log10 values) WHILE tempstep < 1 TempStep = TempStep * 10 INCR mult WEND ' get the magnitude of the step size mag = FIX(LOG10(tempStep)) magPow = 10^mag ' calculate most significant digit of the new step size magMsd = ((tempStep/magPow) + 0.5) ' promote the MSD TO either 1, 2, OR 5 IF (magMsd > 5.0) THEN magMsd = 10.0 ELSEIF (magMsd > 2.0) THEN magMsd = 5.0 ELSEIF (magMsd > 1.0) THEN magMsd = 2.0 END IF StepSize = magMsd*magPow ' reduce scaled up magnitudes if required StepSize = StepSize / 10^mult ' Adjust _min and _max dmin = StepSize * INT(dmin/StepSize) dmax = StepSize * CEIL(dmax/StepSize) FUNCTION = StepSize END FUNCTIONLeave a comment:
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The formula is true, and its generalization may be used for other fractional powers, X ^ s = Exp(s * Log(X)), but I doubt it's used for the special case s = 1 / 2. That case is so common (geometry, statistics, physics, engineering) I imagine it would be especially optimized.Originally posted by Michael Mattias View Post
To go off on a tangent, X ^ n is X times itself n times. Call that the third operation, the first two operations being addition and multiplication. Multiplication is repeated addition and exponential is repeated multiplication. You can imagine a fourth operation which is repeated exponentiation, and ask if it could defined for fractional n as it can be for multiplication and exponentiation. An Internet search on
fourth operation
discovers an article about it – Bing #1, DDG #1, Google #8 (the rankings vary a bit over time).Last edited by Mark Hunter; 12 May 2022, 12:22 AM.Leave a comment:
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Mat() operations are generally classed as "matrix Algebra".Originally posted by Michael Mattias View Post
At a guess, I'd say "trig tables" come from Trigonometry
Computers generall calculate them, using the CORDIC algorithm.
Algebra and Trigonomentry, like Arithmetic are branches of Mathematics.
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Not that those functions are relevant here but you have posed an interesting question.You mean SIN(),COS(),TAN(),ATAN(),SQR(),EXP,LOG,MAT etc are just arithmetic?
SIN(), COS() and TAN() are ratios. SQR() and EXP() are logarithmic ( SQR(X) = EXP(LOG(X)/2). MAT() I think is 'math' or maybe it's just a method (Not a COM method!) of treating sets. I don't know what I would label MAT()
You know, I'm not sure where values in the "trig tables" come from. I've just of always treated them as being fact. Hell, they work here.
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Lines like this:are going to cause trouble with real-world data that may have been rounded. Instead, try something like:Code:IF y3 = a*x3 + b THEN
(where SmallNumber is previously set to a small positive value).Code:IF ABS(y3 - (a*x3 +b)) < SmallNumber THEN
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Mark,
In your edit you did not add REDRAW option to GRAPHIC ATTACH, nor remove the GRAPHIC REDRAW line.
Without the option, GRAPHIC REDRAW has no purpose.
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better graphics scaling ..
Code:#COMPILE EXE #DIM ALL FUNCTION PBMAIN() AS LONG LOCAL x1,x2,x3,y1,y2,y3,a,b AS DOUBLE LOCAL wstrF, wstrL , wstrBet AS WSTRING LOCAL FlagbetX , FlagbetY AS LONG 'Set 1 -- y = 2x where test point is on the line and lies between ' the line points 'Line points ' x2 = 1 : y2 = 2 ' x1 = 4 : y1 = 8 'Test point ' x3 = 3 : y3 = 6 'Set 2 -- answer check correct y = -3x -5 test point is NOT on line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x1 = -5 : y1 = 10 ' x2 = -3 : y2 = 4 'Test point ' x3 = -2 : y3 = 7 'Set 3 -- answer check correct y = 6x +4 test point is on line but not between line points ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = -5 : y2 = -26 ' x1 = -2 : y1 = -8 'Test point ' x3 = -7 : y3 = -38 'Set 4 -- answer check correct y = 6x +4 test point is on line and lies between ' the line points ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = -5 : y2 = -26 ' x1 = -2 : y1 = -8 'Test point ' x3 = -3 : y3 = -14 'Set 5 -- answer check correct y = 4.5x - 24 test point is NOT on the line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x2 = 6 : y2 = 3 ' x1 = 4 : y1 = -6 'Test point ' x3 = 3.6 : y3 = -10 'Set 6 -- answer check correct y = 1.5x - 2.5 test point is NOT on the line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points x2 = 3 : y2 = 2 x1 = 5 : y1 = 5 'Test point x3 = 4 : y3 = 4 wstrF = "The equation for the line (" & STR$(x1,4) & " , " & _ STR$(y1,4) & ") - (" & STR$(x2,4) & " , " & STR$(y2,4) & ") is:" & $LF wstrL = $LF & "The point (" & STR$(x3,4) & " ," & STR$(y3,4) & ") " IF x1 = x2 THEN 'line is vertical wstrF &= "X = " & STR$(x1,3) IF x3 = x1 THEN 'point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE wstrF &= "Y=" IF y1 = y2 THEN ' line is horizontal wstrF &= "0x + " & STR$(y1,4) IF y3 = y1 THEN ' point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE ' line is neither horizontaol nor vertical a = (y2-y1)/(x2-x1) b = (x2*y1-x1*y2)/(x2-x1) wstrF &= STR$(a,4) & "X " & IIF$(b>=0," +"," ") & STR$(b,3) IF y3 = a*x3 + b THEN wstrL &= " is on the line" ' check if x3 is between x1 and x2 FlagbetX = 0 IF x2 >= x1 THEN IF x3 >= x1 THEN IF x3 <= x2 THEN FlagbetX = 1 END IF END IF ELSE IF x3 >= x2 THEN IF x3 <= x1 THEN FlagbetX = 1 END IF END IF END IF ' check if y3 is between y1 and y2 FlagbetY = 0 IF y2 >= y1 THEN IF y3 >= y1 THEN IF y3 <= y2 THEN FlagbetY = 1 END IF END IF ELSE IF y3 >= y2 THEN IF y3 <= y1 THEN FlagbetY = 1 END IF END IF END IF wstrBet = $CRLF +"But it does NOT lies between the given Line points" IF FlagbetX + FlagbetY = 2 THEN wstrBet = $CRLF + "And it also lies between the given Line points" END IF ELSE wstrl &= " is NOT on the line" END IF END IF END IF ' draw the graphics ' pirated from ' https://forum.powerbasic.com/forum/user-to-user-discussions/powerbasic-for-windows/816259-how-to-draw-a-polygon-graphically?p=816366#post816366 LOCAL hGraph AS DWORD LOCAL xmin,xmax ,ymin, ymax AS DOUBLE ' obtain the min and max coord of the 3 points ' to do the scaling xmin = MIN(x1,x2,x3) ymin = MIN(y1,y2,y3) xmax = MAX(x1,x2,x3) ymax = MAX(y1,y2,y3) GRAPHIC WINDOW NEW "Line and points",100,100,400,400 TO hGraph ' Scale Windows so that points coordinates fit nicely GRAPHIC SCALE (xmin-5, ymax+5) - (xmax+5, ymin-5) GRAPHIC COLOR %RGB_RED 'Draw the line GRAPHIC LINE (x1,y1) - (x2,y2) ' draw the points in large dots GRAPHIC BOX (x1-.2,y1-.2) - _ (x1+.2, y1+.2),100,%RGB_BLUE,%RGB_BLUE GRAPHIC BOX (x2-.2,y2-.2) - _ (x2+.2, y2+.2),100,%RGB_BLUE,%RGB_BLUE GRAPHIC BOX (x3-.2,y3-.2) - _ (x3+.2, y3+.2),100,%RGB_LIME,%RGB_LIME ' display messagebox ? wstrF & wstrL & wstrBet GRAPHIC WAITKEY$ GRAPHIC WINDOW END hGraph END FUNCTIONLeave a comment:
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Thanks, I added it in an edit.Originally posted by Mike Doty View PostLeave a comment:
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Another way without all of those IFs.
'Code:FlagbetX = (x3 <= MAX(x1,x2)) AND (x3 >= MIN(x1,x2)) FlagbetY = (y3 <= MAX(y1,y2)) AND (y3 >= MIN(y1,y2)) IF NOT FlagbetX THEN wstrL &= $LF & "X = " & STR$(x3,4) & " is outside of the X bounds of the line" IF NOT FlagbetY THEN wstrL &= $LF & "Y = " & STR$(y3,4) & " is outside of the Y bounds of the line" '
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maybe like this
Code:#COMPILE EXE #DIM ALL FUNCTION PBMAIN() AS LONG LOCAL x1,x2,x3,y1,y2,y3,a,b AS DOUBLE LOCAL wstrF, wstrL , wstrBet AS WSTRING LOCAL FlagbetX , FlagbetY AS LONG 'Set 1 'Line points ' x1 = 1 : y1 = 2 ' x2 = 4 : y2 = 8 'Test point ' x3 = 3 : y3 = 6 'Set 2 -- answer check correct y = -3x -5 test point is NOT on line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x1 = -5 : y1 = 10 ' x2 = -3 : y2 = 4 'Test point ' x3 = -2 : y3 = 7 'Set 3 -- answer check correct y = 6x +4 test point is on line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points ' x1 = -5 : y1 = -26 ' x2 = -2 : y2 = -8 'Test point ' x3 = -20 : y3 = -116 'Set 4 -- answer check correct y = 6x +4 test point is on line ' https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-11-2.html#WS1 'Line points x1 = -5 : y1 = -26 x2 = -2 : y2 = -8 'Test point x3 = -3 : y3 = -14 wstrF = "The equation for the line (" & STR$(x1,4) & " , " & STR$(y1,4) & ") - (" & STR$(x2,4) & " , " & STR$(y2,4) & ") is:" & $LF wstrL = $LF & "The point (" & STR$(x3,4) & " ," & STR$(y3,4) & ") is " IF x1 = x2 THEN 'line is vertical wstrF &= "X = " & STR$(x1,3) IF x3 = x1 THEN 'point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE wstrF &= "Y=" IF y1 = y2 THEN ' line is horizontal wstrF &= "0x + " & STR$(y1,4) IF y3 = y1 THEN ' point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE ' line is neither horizontaol nor vertical a = (y2-y1)/(x2-x1) b = (x2*y1-x1*y2)/(x2-x1) wstrF &= STR$(a,4) & "X " & IIF$(b>=0," +"," ") & STR$(b,3) IF y3 = a*x3 + b THEN wstrL &= " is on the line" ' check if x3 is between x1 and x2 FlagbetX = 0 IF x2 >= x1 THEN IF x3 >= x1 THEN IF x3 <= x2 THEN FlagbetX = 1 END IF END IF ELSE IF x3 >= x2 THEN IF x3 <= x1 THEN FlagbetX = 1 END IF END IF END IF ' check if y3 is between y1 and y2 FlagbetY = 0 IF y2 >= y1 THEN IF y3 >= y1 THEN IF y3 <= y2 THEN FlagbetY = 1 END IF END IF ELSE IF y3 >= y2 THEN IF y3 <= y1 THEN FlagbetY = 1 END IF END IF END IF wstrBet = $CRLF +"But it does NOT lies between the given Line points" IF FlagbetX + FlagbetY = 2 THEN wstrBet = $CRLF + "And it also lies between the given Line points" END IF ELSE wstrl &= " is NOT on the line" END IF END IF END IF ? wstrF & wstrL & wstrBet END FUNCTIONLeave a comment:
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Thank you Sir Stuart, I will try to do the check of x3 is between x1 and x2 as well as y3 is between x1 and x2 to see if I can do the math!Leave a comment:
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You mean SIN(),COS(),TAN(),ATAN(),SQR(),EXP,LOG,MAT etc are just arithmetic?Originally posted by Michael Mattias View Post
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Here ya go.
Note this determines if Point 3 lies on the line through Points 1 and 2 (i.e. the line described by the equation), not the line between points 1 and 2.
If you require the latter you would need to also check whether x3 lies within x1 and x2 and whether y3 lies within y1 and y2!
'Code:#COMPILE EXE FUNCTION PBMAIN() AS LONG LOCAL x1,x2,x3,y1,y2,y3,a,b AS DOUBLE LOCAL wstrF, wstrL AS WSTRING 'Line points x1 = 1 : y1 = 2 x2 = 2 : y2 = 4 'Test point x3 = 3 : y3 = 6 wstrF = "The equation for the line (" & STR$(x1,4) & " , " & STR$(y1,4) & ") - (" & STR$(x2,4) & " , " & STR$(y2,4) & ") is:" & $LF wstrL = $LF & "The point (" & STR$(x3,4) & " ," & STR$(y3,4) & ") is " IF x1 = x2 THEN 'line is vertical wstrF &= "X = " & STR$(x1,3) IF x3 = x1 THEN 'point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE wstrF &= "Y=" IF y1 = y2 THEN ' line is horizontal wstrF &= "0x + " & STR$(y1,4) IF y3 = y1 THEN ' point is on line wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF ELSE ' line is neither horizontaol nor vertical a = (y2-y1)/(x2-x1) b = (x2*y1-x1*y2)/(x2-x1) wstrF &= STR$(a,4) & "X " & IIF$(b>=0," +"," ") & STR$(b,3) IF y3 = a*x3 + b THEN wstrL &= " is on the line" ELSE wstrl &= " is NOT on the line" END IF END IF END IF ? wstrF & wstrL END FUNCTION 'Leave a comment:
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