A Point3.T is a point in 3-space. It is represented as a record with three components, x, y, and z, all holding real values.

INTERFACE Point3;

TYPE
  T = RECORD
    x,y,z : REAL;
  END;

CONST
  Origin = T {0.0, 0.0, 0.0};
  Min    = T {FIRST(REAL), FIRST(REAL), FIRST(REAL)};
  Max    = T {LAST (REAL), LAST (REAL), LAST (REAL)};

Origin is the origin of the coordinate system. Min and Max are used in bounding box calculations to represent imaginary smallest and largest points.

PROCEDURE Plus (a, b : T) : T;

Plus(a,b) returns the sum of the points a and b.

PROCEDURE Minus (a, b : T) : T;

Minus(a,b) returns the difference between a and b.

PROCEDURE TimesScalar (a : T; x : REAL) : T;

TimesScalar(a,s) returns a with each component multiplied with the scalar value s.

PROCEDURE MidPoint (a, b : T) : T;

MidPoint(a,b) returns the point in the middle between a and b.

PROCEDURE Distance (a, b : T) : REAL;

Distance(a,b) returns the distance between a and b.

PROCEDURE ToText (a : T) : TEXT;

ToText(a) returns a textual representation of a; for example, ToText(T{2.0,3.0,5.0}) returns the text (2.0,3.0,5.0) .

PROCEDURE Length (a : T) : REAL;

Length(a) returns the length of the vector a.

PROCEDURE DotProduct (a, b : T) : REAL;

Returns the dot product of a and b. See [Foley] p. 1094ff for an explanation of the geometric significance of dot products.

PROCEDURE CrossProduct (a, b : T) : T;

Returns the cross product of a and b. See [Foley] p. 1104ff for an explanation of the geometric significance of cross products. One important property is that $a \times b$ is orthogonal to the plane described by the vectors a and b.

PROCEDURE OrthoVector (a : T) : T;

Returns a unit vector which is orthogonal to n. There are infinitely many such vectors, OrthoVector will return one of them.

PROCEDURE ScaleToLen (a : T; len : REAL) : T;

Returns a vector parallel to a with length len.

END Point3.