Des vecteurs et des repères (mp-geom2d)
Auteur ou autrice : Jean-Michel Sarlat.
Mise en ligne le 19 mai 2025
mp-geom2d a été écrit avec le but de proposer des macros MetaPost permettant de réaliser une figure de géométrie en collant d’assez près à une description impérative :
- Soit $A$ le point de coordonnées $(2,3)$.
- Soit $B$ le point de coordonnées $(4,5)$.
- Trace la droite $(A,B)$.
- ...
Ici, on montre les exemples de la galerie de la documentation à la fois dans l’interface en français et celle en anglais.
Code
input geom2d;
labeloffset := 4;
gddU:=1.cm;
beginfig(1);
O = Point(0,0);
I = Point(1,0);
J = Point(0.3,0.8);
M = PointDansRepere(5,3,O,I,J);
H = PointDansRepere(5,0,O,I,J);
K = PointDansRepere(0,3,O,I,J);
O' = Point(3,2);
I' = Point(3.7,1.8);
J' = Point(2.8,3);
pair Mt;
Mt = CoordonneesRepere(M,O',I',J');
H' = PointDansRepere(xpart Mt,0,O',I',J');
K' = PointDansRepere(0,ypart Mt,O',I',J');
Repere(8,6,1.5,1.5,1,1);
Debut;
trace Droite(O,I);
trace Droite(O,J);
trace Droite(O',I');
trace Droite(O',J');
trace Pt(K)--Pt(M)--Pt(H) dashed evenly;
trace Pt(K')--Pt(M)--Pt(H') dashed evenly;
marque.urt "M";
drawoptions(withpen pencircle scaled 1pt withcolor DodgerBlue);
fleche Segment(O,K);
fleche Segment(O,H);
fleche Segment(O,M);
drawoptions(withpen pencircle scaled 1pt withcolor LimeGreen);
fleche Segment(O',M);
fleche Segment(O',H');
fleche Segment(O',K');
drawoptions(withpen pencircle scaled 1.5pt withcolor Crimson);
fleche Segment(O,I);
fleche Segment(O,J);
fleche Segment(O',I');
fleche Segment(O',J');
drawoptions(withpen pencircle scaled 1pt withcolor LightCoral);
fleche Segment(O,O');
drawoptions();
marque.llft "O";
marque.llft "O'";
label.bot(textext("\(x\)"), PtR(H));
label.lft(textext("\(y\)"), PtR(K));
label.bot(textext("\(\vec\imath\)"), PtR(I));
label.lft(textext("\(\vec\jmath\)"), PtR(J));
label.bot(textext("\(x'\)"), PtR(H'));
label.urt(textext("\(y'\)"), PtR(K'));
label.bot(textext("\(\vec\imath'\)"), PtR(I'));
label.lft(textext("\(\vec\jmath'\)"), PtR(J'));
Fin;
endfig;
end
%%%% English version
labeloffset := 4;
gddU:=1.cm;
beginfig(1);
O = Point(0,0);
I = Point(1,0);
J = Point(0.3,0.8);
M = PointInBasis(5,3,O,I,J);
H = PointInBasis(5,0,O,I,J);
K = PointInBasis(0,3,O,I,J);
O' = Point(3,2);
I' = Point(3.7,1.8);
J' = Point(2.8,3);
pair Mt;
Mt = CoordinatesInBasis(M,O',I',J');
H' = PointInBasis(xpart Mt,0,O',I',J');
K' = PointInBasis(0,ypart Mt,O',I',J');
Frame(8,6,1.5,1.5,1,1);
gddBegin;
gddDraw Line(O,I);
gddDraw Line(O,J);
gddDraw Line(O',I');
gddDraw Line(O',J');
gddDraw Pt(K)--Pt(M)--Pt(H) dashed evenly;
gddDraw Pt(K')--Pt(M)--Pt(H') dashed evenly;
gddMark.urt "M";
drawoptions(withpen pencircle scaled 1pt withcolor DodgerBlue);
gddArrow Segment(O,K);
gddArrow Segment(O,H);
gddArrow Segment(O,M);
drawoptions(withpen pencircle scaled 1pt withcolor LimeGreen);
gddArrow Segment(O',M);
gddArrow Segment(O',H');
gddArrow Segment(O',K');
drawoptions(withpen pencircle scaled 1.5pt withcolor Crimson);
gddArrow Segment(O,I);
gddArrow Segment(O,J);
gddArrow Segment(O',I');
gddArrow Segment(O',J');
drawoptions(withpen pencircle scaled 1pt withcolor LightCoral);
gddArrow Segment(O,O');
drawoptions();
gddMark.llft "O";
gddMark.llft "O'";
label.bot(textext("\(x\)"), PtR(H));
label.lft(textext("\(y\)"), PtR(K));
label.bot(textext("\(\vec\imath\)"), PtR(I));
label.lft(textext("\(\vec\jmath\)"), PtR(J));
label.bot(textext("\(x'\)"), PtR(H'));
label.urt(textext("\(y'\)"), PtR(K'));
label.bot(textext("\(\vec\imath'\)"), PtR(I'));
label.lft(textext("\(\vec\jmath'\)"), PtR(J'));
gddEnd;
endfig;
end
Mots clés : géométrievecteurrepèremp-geom2d
Cet exemple fait partie de la collection d’exemples Documentation de mp-geom2d.