#### 10.10.15 DrawPlan

• DrawPlan( <plane>, <3Dvector>, <length1>, <length2> [, type] )
• Description: permits to represent a plane of the space, the parameter <plane> is in the form [3Dpoint, 3D normal vector], let be $A$ the point and $u$ the 3D normal vector, The following parameter is a vector of the plane (call it $v$), the macro computes the vectorial product $w=u\wedge v$ and determine the following parallelogram:

 \begin{texgraph}[name=drawplan1,export=pgf]   view(-5,5,-5,5),Marges(0,0,0,0), size(8), DotStyle:=cross,   A:=0, M4:=-4+3*i, M1:=-2-3*i, M2:=4-3*i, M3:=2+3*i,   LabelDot(A,"$A$","NE",1), Arrows:=1, Ligne([A,A+2*i],0),   Width:=4, Arrows:=0, angleD(A+i,A,A-1, 0.25),   LabelStyle:=scriptsize, LabelDot(A+i,"$\vec{u}$","O"),   Width:=8, Color:=red, Arrows:=1, Ligne([M1,M2],0),   Width:=4,Color:=black, LabelStyle:=left,   LabelDot((M1+M2)/2,"$\dfrac{L_1\cdot\vec{v}}{\|\vec{v}\|}$","S"),   Width:=8,Color:=red, Ligne([M2,M3],0),   Width:=4,Color:=black,LabelStyle:=top,   LabelDot((M2+M3)/2,"$\dfrac{L2\cdot\vec{w}}{\|\vec{w}\|}$","E"),   Arrows:=0,   LabelDot(M4,"$M4$","NO",1),   LabelDot(M1,"$M1$","SO",1),   LabelDot(M2,"$M2$","SE",1),   LabelDot(M3,"$M3$","NE",1),   Ligne([M3,M4,M1],0)   \end{texgraph}

The drawplan macro

where L1 is the parameter <length1> and L2 the parameter <length2>. If the last parameter <type> is not present, then this is the parallelogram that is drawn. The possible type values are : -1, -2, -3, -4, 1, 2, 3, 4. that is giving (the point $A$, the vector $u$ and the right angle have been added):

 \begin{texgraph}[name=drawplan2,export=pgf,file]   Cmd        [Fenetre(-6+5.5*i,6-5.5*i,0.625+0.625*i), Marges(0,0,0,0), Border(0)];           [OriginalCoord(1),IdMatrix()];           [theta:=0.0872, phi:=1.1345, IdMatrix3D(), ModelView(ortho)];   Var       A = [-4.5*i,4];       B = [-4.5*i,-1];       C = [0,-5];   Mac       plan = [ a:=%1, type:=%2, Arrows:=0,            LabelDot(Proj3D(%1),"$A$","E",1,0.2),            Width:=8,            DrawPlan( [a,vecK], vecJ, 2, 2, type),            angleD( Proj3D(a+vecK), Proj3D(a), Proj3D(a-vecJ), 0.15),            Arrows:=1,            Ligne( Proj3D( [a, a+vecK]),0),            LabelDot( Proj3D([a+vecK]), "$\vec{u}$", "N",0)           ];   Graph objet1 = [           Width:=8, Marges(0,0,0,0), size(7.5),           plan(A,1), plan( A+3*vecJ,2), plan( A+6*vecJ,3),plan( A+9*vecJ,4),           plan(B,-1), plan( B+3*vecJ,-2), plan( B+6*vecJ,-3),plan( B+9*vecJ,-4),           plan(C),           Arrows:=0,LabelSize:=footnotesize,           Label(-4.5+2.7564*i,"type=$1$"),           Label(-1.2529+2.7564*i,"type=$2$"),           Label(1.5+2.7564*i,"type=$3$"),           Label(4.4824+2.7564*i,"type=$4$"),           Label(-4.7471-2.0032*i,"type=$-1$"),           Label(-1.5-2.0032*i,"type=$-2$"),           Label(1.5-2.0032*i,"type=$-3$"),           Label(4.2529-2.0032*i,"type=$-4$"),           Label(-0.2471-5.2532*i,"no type")           ];   \end{texgraph}

Planes types