### Math: how calculate the line dots?

the line have origin and destion points.
how can i calculate the dots between the line origin and destination.
i create these code:
 ``123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384`` ``````#include #include #include #include using namespace std; HDC WindowHDC=NULL; struct Coordenates { int X=0; int Y=0; int Z=0; }; //get the X, Y and Z distance between the Destination and Origin line points: Coordenates DefPosition3D(Coordenates Origin, Coordenates Destiny) { Coordenates distance; distance.X = Destiny.X - Origin.X; distance.Y = Destiny.Y - Origin.Y; distance.Z = Destiny.Z - Origin.Z; return distance; } //get the step incremention: Coordenates InCrement(Coordenates DefPosition, Coordenates Steps ) { Coordenates inc ; if(inc.X>0) inc.X = DefPosition.X / Steps.X; if(inc.Y>0) inc.Y = DefPosition.Y / Steps.Y; if(inc.Z>0) inc.Z = DefPosition.Z / Steps.Z; return inc; } void DrawLineDots(Coordenates Origin, Coordenates Destination) { Coordenates Steps; Coordenates inc; //get the steps between Destination and origin: Steps = DefPosition3D(Origin, Destination); //get increment steps: inc =InCrement(Steps, Steps); Coordenates nextpoint; int X ; int Y; int Z; //get the line dots: for (X = 0; X< Steps.X ; X++) { for (Y = 0; Y< Steps.Y;Y++) { for (Z = 0; Z< Steps.Z;Z++) { nextpoint.X = round(nextpoint.X + Steps.X); nextpoint.Y = round(nextpoint.Y + Steps.Y); nextpoint.Z = round(nextpoint.Z + Steps.Z); SetPixel(WindowHDC,0,0,RGB(255,0,0)); } } } } int main() { //getting the HDC Console Window: WindowHDC=GetDC(GetConsoleWindow()); do { DrawLineDots({0,10,0},{100,10,0}); }while(!(GetKeyState(13) & 0x8000));//press escape for exit return 0; }``````

so my question is: how can i calculate the line dots between origin and destination line?
Well, your call to SetPixel doesn't seem to use any information about the point you have just calculated and I'm not sure why your call to InCrement uses two identical arguments.

Also, you seem to be using 3-d coordinates for a 2-d plot, a straight line has ONE increment parameter, not 3, and you seem to be using round() on ints.
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not sure what you are doing, but I would suggest..

dist = distance between start and end.
for(0 to distance)
{
///what you have now, add x,y,z deltas to last point, from start
}
the triple nested loop just looks wrong to me. I could be not seeing something there, but ???
the deltas and points need to be doubles, so you can add like 0.0001 or whatever small change that accumulates to say draw a line from 0,0,0 to 0,1,10000000 or whatever :)
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With <windows.h>, you could use the LineDDA function.
https://docs.microsoft.com/en-us/windows/win32/api/wingdi/nf-wingdi-linedda
Forget figuring it out yourself. Since you are using the Windows GDI API, use MoveToEx|https://docs.microsoft.com/en-us/windows/win32/api/wingdi/nf-wingdi-movetoex and LineTo|https://docs.microsoft.com/en-us/windows/win32/api/wingdi/nf-wingdi-lineto.

If you really want to put your own pixels/whatever then look up “Bresenham’s Line Algorithm” (fast and simple) and “Wu’s Line Algorithm” (for antialiasing).

Hope this helps.
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Only the calculations.
 ``12345678910111213141516171819202122232425262728293031323334353637383940`` ``````#include #include using namespace std; struct point { float x,y,z; } ; float distance(point p1,point p2) { return sqrt( (p1.x-p2.x)* (p1.x-p2.x) + (p1.y-p2.y)* (p1.y-p2.y) + (p1.z-p2.z)* (p1.z-p2.z)); } point lineto(point fp,point p,float length) { point res; float L=distance(fp,p); res.x=fp.x+length*(p.x-fp.x)/L; res.y=fp.y+length*(p.y-fp.y)/L; res.z=fp.z+length*(p.z-fp.z)/L; return res; } int main() { point origin={0,0,0}; point destination={100,200,50}; point t=origin; float dst=distance(origin,destination); for (int i=0;i<=dst;i++) { t=lineto(t,destination,1); cout<
i did some changes.... i need ask: how can i convert the Z to X,Y?
i did:
`SetPixel(WindowHDC,t.x/t.z,t.y/t.z,color);`
X/Z and Y/Z.. is these correct?
heres the result from:
 ``12`` ``````point origin={0,100,1}; point destination={500,100,2};``````

https://imgur.com/Qt7DVth
is these correct? the Z seems more big than i thot :(
heres the entire code now:
 ``123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869`` ``````#include #include #include #include using namespace std; struct point { float x,y,z; } ; float distance(point p1,point p2) { return sqrt( (p1.x-p2.x)* (p1.x-p2.x) + (p1.y-p2.y)* (p1.y-p2.y) + (p1.z-p2.z)* (p1.z-p2.z)); } point lineto(point fp,point p,float length) { point res; float L=distance(fp,p); res.x=fp.x+length*(p.x-fp.x)/L; res.y=fp.y+length*(p.y-fp.y)/L; res.z=fp.z+length*(p.z-fp.z)/L; return res; } vector GetPointsLine(point origin,point destination) { point t=origin; vector coordenates; float dst=distance(origin,destination); for (int i=0;i<=dst;i++) { t=lineto(t,destination,1); coordenates.push_back(t); } return coordenates; } vector DrawLine(HDC WindowHDC,point origin,point destination,COLORREF color=RGB(255,0,0) ) { point t=origin; vector coordenates; float dst=distance(origin,destination); for (int i=0;i<=dst;i++) { t=lineto(t,destination,1); coordenates.push_back(t); if(t.x>0 && t.y>0) SetPixel(WindowHDC,t.x/t.z,t.y/t.z,color); } return coordenates; } int main() { //getting the HDC Console Window: HDC WindowHDC=GetDC(GetConsoleWindow()); point origin={0,100,1}; point destination={500,100,2}; do { DrawLine(WindowHDC,origin,destination); }while(!(GetKeyState(13) & 0x8000));//press escape for exit cout<<"Press return to end . . ."<
What do you mean by "convert the Z to X,Y"?
the screen just use X and Y... so where is the Z?
(yes it's 3D... i'm doing these for 3D)
how convert 3D to 2D?
i found my error...
for convert 3D to 2D we must:
2D.X = 3D.X * FocalDistance / 3D.Z
2D.Y = 3D.Y * FocalDistance / 3D.Z

i belive: the FocalDistance is the distance between our eye and the 3D World.
i accept correction. i use '100' on code.
see these result:
 ``12`` ``````point origin={0,100,0}; point destination={500,110,-1};``````

https://imgur.com/VKFyt4K

 ``1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677`` ``````#include #include #include #include using namespace std; struct point { float x,y,z; } ; float distance(point p1,point p2) { return sqrt( (p1.x-p2.x)* (p1.x-p2.x) + (p1.y-p2.y)* (p1.y-p2.y) + (p1.z-p2.z)* (p1.z-p2.z)); } point lineto(point fp,point p,float length) { point res; float L=distance(fp,p); res.x=fp.x+length*(p.x-fp.x)/L; res.y=fp.y+length*(p.y-fp.y)/L; res.z=fp.z+length*(p.z-fp.z)/L; return res; } vector GetPointsLine(point origin,point destination) { point t=origin; vector coordenates; float dst=distance(origin,destination); for (int i=0;i<=dst;i++) { t=lineto(t,destination,1); coordenates.push_back(t); } return coordenates; } vector DrawLine(HDC WindowHDC,point origin,point destination,COLORREF color=RGB(255,0,0) ) { float FocalDistance =100; //for convert 3D to 2D we must: //2D.X = 3D.X * FocalDistance / 3D.Z //2D.Y = 3D.Y * FocalDistance / 3D.Z point t=origin; vector coordenates; float dst=distance(origin,destination); for (int i=0;i<=dst;i++) { t=lineto(t,destination,1); coordenates.push_back(t); if(t.z>0) SetPixel(WindowHDC,t.x/t.z*FocalDistance,t.y/t.z*FocalDistance,color); else SetPixel(WindowHDC,t.x,t.y,color); } return coordenates; } int main() { //getting the HDC Console Window: HDC WindowHDC=GetDC(GetConsoleWindow()); point origin={0,100,0}; point destination={500,110,-1}; do { DrawLine(WindowHDC,origin,destination); }while(!(GetKeyState(13) & 0x8000));//press escape for exit cout<<"Press return to end . . ."<
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tomorrow i will test the next step and share ;)

You can only plot x and y.
The .z value can be used to simulate 3d, for instance instead of SetPixel, you could use ellipse to draw small circles which change size according to the .z value to give the effect of the dots going into the distance. (getting smaller).

simulated 3d also involves some angle work to make it look right. Something square in 2d looked at in the xz plane for instance is a slanted thing in 3d

 ``` /-------/ //angles and shifting / / --------- | | | | | | --------- ```
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3D Rotation:
https://imgur.com/qOgUuPf

2D Rotation:
https://imgur.com/irN1i7N

now i will create a new topic.
thanks for all to all
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