Find the intersection of a line with a plane: Difference between revisions

=={{header|Modula-2}}==

<lang modula2>MODULE LinePlane;

FROM RealStr IMPORT RealToStr;

FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

TYPE

Vector3D = RECORD

x,y,z : REAL;

END;

PROCEDURE Minus(lhs,rhs : Vector3D) : Vector3D;

VAR out : Vector3D;

BEGIN

RETURN Vector3D{lhs.x-rhs.x, lhs.y-rhs.y, lhs.z-rhs.z};

END Minus;

PROCEDURE Times(a : Vector3D; s : REAL) : Vector3D;

BEGIN

RETURN Vector3D{a.x*s, a.y*s, a.z*s};

END Times;

PROCEDURE Dot(lhs,rhs : Vector3D) : REAL;

BEGIN

RETURN lhs.x*rhs.x + lhs.y*rhs.y + lhs.z*rhs.z;

END Dot;

PROCEDURE ToString(self : Vector3D);

VAR buf : ARRAY[0..63] OF CHAR;

BEGIN

WriteString("(");

RealToStr(self.x,buf);

WriteString(buf);

WriteString(", ");

RealToStr(self.y,buf);

WriteString(buf);

WriteString(", ");

RealToStr(self.z,buf);

WriteString(buf);

WriteString(")");

END ToString;

PROCEDURE IntersectPoint(rayVector,rayPoint,planeNormal,planePoint : Vector3D) : Vector3D;

VAR

diff : Vector3D;

prod1,prod2,prod3 : REAL;

BEGIN

diff := Minus(rayPoint,planePoint);

prod1 := Dot(diff, planeNormal);

prod2 := Dot(rayVector, planeNormal);

prod3 := prod1 / prod2;

RETURN Minus(rayPoint, Times(rayVector, prod3));

END IntersectPoint;

VAR ip : Vector3D;

BEGIN

ip := IntersectPoint(Vector3D{0.0,-1.0,-1.0},Vector3D{0.0,0.0,10.0},Vector3D{0.0,0.0,1.0},Vector3D{0.0,0.0,5.0});

WriteString("The ray intersects the plane at ");

ToString(ip);

WriteLn;

ReadChar;

END LinePlane.</lang>