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csMath3 Class Reference

Various assorted 3D mathematical functions. More...

#include <math3d.h>

List of all members.

Static Public Methods

int WhichSide3D (const csVector3 &p, const csVector3 &v1, const csVector3 &v2)

Tests which side of a plane the given 3D point is on. More...

bool Visible (const csVector3 &p, const csVector3 &t1, const csVector3 &t2, const csVector3 &t3)

Tests if the front face of a triangle is visible from the given point. More...

bool Visible (const csVector3 &p, const csPlane3 &pl)

Check if the plane is visible from the given point. More...

bool FindIntersection (const csVector3 tri1[3], const csVector3 tri2[3], csVector3 line[2])

Calculate the line, that is the result of the Intersection of triangle 1 and triangle 2. More...

void Between (const csVector3 &v1, const csVector3 &v2, csVector3 &v, float pct, float wid)

Calculates a vector lying a specified distance between two other vectors. More...

void SetMinMax (const csVector3 &v, csVector3 &min, csVector3 &max)

Set the min and max vector if this vector exceeds their current limits. More...

float Area3 (const csVector3 &a, const csVector3 &b, const csVector3 &c)

Compute twice the signed area of triangle composed by three points. More...

void CalcNormal (csVector3 &norm, const csVector3 &v1, const csVector3 &v2, const csVector3 &v3)

Calculate a plane normal given three vectors. More...

void CalcNormal (csVector3 &norm, const csVector3 &v, const csVector3 &u)

Compute the normal given two (u,v) vectors. More...

void CalcPlane (const csVector3 &v1, const csVector3 &v2, const csVector3 &v3, csVector3 &normal, float &D)

Calculate the plane equation given three vectors. More...

bool PlanesEqual (const csPlane3 &p1, const csPlane3 &p2)

Check if two planes are almost equal. More...

bool PlanesClose (const csPlane3 &p1, const csPlane3 &p2)

Check if two planes are close together. More...

int OuterPlanes (const csBox3 &box1, const csBox3 &box2, csPlane3 *planes)

Calculate the set of outer planes between the two boxes. More...

int FindObserverSides (const csBox3 &box1, const csBox3 &box2, int *sides)

Find all observer sides on the first box that can see the other box. More...

void SpherePosition (float angle_xz, float angle_vert, csVector3 &pos)

Given two angles in radians, calculate the position on the sphere around (0,0,0) with radius 1. More...

Detailed Description

Various assorted 3D mathematical functions.

This is a static class and contains only static member functions.

Member Function Documentation

float csMath3::Area3 ( const csVector3 & a,

const csVector3 & b,

const csVector3 & c ) [inline, static]

Compute twice the signed area of triangle composed by three points.
This function returns 2 x the area of the triangle formed by the points a, b, and c.

void csMath3::Between ( const csVector3 & v1,

const csVector3 & v2,

csVector3 & v,

float pct,

float wid ) [static]

Calculates a vector lying a specified distance between two other vectors.
Given vectors v1 and v2, this function will calculate and return vector v lying between them. If pct != -1, vector v will be the point which is pct % of the way from v1 to v2. Otherwise, if pct equals -1, v will be the point along 'v1-v2' which is distance wid from v1.

void csMath3::CalcNormal ( csVector3 & norm,

const csVector3 & v,

const csVector3 & u ) [inline, static]

Compute the normal given two (u,v) vectors.
This function will calculate the normal to a polygon with two edges represented by v and u. The result is stored in norm.

void csMath3::CalcNormal ( csVector3 & norm,

const csVector3 & v1,

const csVector3 & v2,

const csVector3 & v3 ) [inline, static]

Calculate a plane normal given three vectors.
This function will calculate the normal to the plane formed by vectors v1, v2, and v3, and store the result in norm.

void csMath3::CalcPlane ( const csVector3 & v1,

const csVector3 & v2,

const csVector3 & v3,

csVector3 & normal,

float & D ) [inline, static]

Calculate the plane equation given three vectors.
Given three vectors v1, v2, and v3, forming a plane, this function will calculate the plane equation and return the result in 'normal' and 'D'.

bool csMath3::FindIntersection ( const csVector3 tri1[3],

const csVector3 tri2[3],

csVector3 line[2] ) [static]

Calculate the line, that is the result of the Intersection of triangle 1 and triangle 2.
This Method returns false, if there is no intersection. If there is an intersection, the start of the line is in line[0] and the end of the line is in line[1] and the method return true;

int csMath3::FindObserverSides ( const csBox3 & box1,

const csBox3 & box2,

int * sides ) [static]

Find all observer sides on the first box that can see the other box.
Sides are numbered like this: 0=MinX(), 1=MaxX(), 2=MinY(), 3=MaxY(), 4=MinZ(), 5=MaxZ(). The given array should have place for 6 sides. This function returns the number of observer sides.

int csMath3::OuterPlanes ( const csBox3 & box1,

const csBox3 & box2,

csPlane3 * planes ) [static]

Calculate the set of outer planes between the two boxes.
Is something does not intersect this set of planes then it will not be between the two boxes. The given array of planes should have place for at least eight planes. This function returns the number of planes that are put in 'planes'.

bool csMath3::PlanesClose ( const csPlane3 & p1,

const csPlane3 & p2 ) [static]

Check if two planes are close together.
Two planes are close if there are almost equal OR if the normalized versions are almost equal.

bool csMath3::PlanesEqual ( const csPlane3 & p1,

const csPlane3 & p2 ) [inline, static]

Check if two planes are almost equal.
The function returns true iff each component of the plane equation for one plane is within .001 of the corresponding component of the other plane.

void csMath3::SetMinMax ( const csVector3 & v,

csVector3 & min,

csVector3 & max ) [inline, static]

Set the min and max vector if this vector exceeds their current limits.
This function will check each component of vector v against the maximum and minimum values specified by min and max. If the limits are exceeded, new min or max values will be set.

void csMath3::SpherePosition ( float angle_xz,

float angle_vert,

csVector3 & pos ) [static]

Given two angles in radians, calculate the position on the sphere around (0,0,0) with radius 1.
The first angle is the angle along the horizontal (x/z) plane. The second angle is the vertical angle.

bool csMath3::Visible ( const csVector3 & p,

const csPlane3 & pl ) [inline, static]

Check if the plane is visible from the given point.
This function does a back-face culling test to see whether the front face of plane pl is visible from point p.

bool csMath3::Visible ( const csVector3 & p,

const csVector3 & t1,

const csVector3 & t2,

const csVector3 & t3 ) [static]

Tests if the front face of a triangle is visible from the given point.
Visibility test (backface culling) to see if the triangle formed by t1, t2, and t3 is visible from point p.

int csMath3::WhichSide3D ( const csVector3 & p,

const csVector3 & v1,

const csVector3 & v2 ) [inline, static]

Tests which side of a plane the given 3D point is on.
Return -1 if point p is left of plane '0-v1-v2', 1 if point p is right of plane '0-v1-v2', or 0 if point p lies on plane '0-v1-v2'. Plane '0-v1-v2' is the plane passing through points <0,0,0>, v1, and v2.
Warning: the result of this function when 'p' is exactly on the plane 0-v1-v2 is undefined. It should return 0 but it will not often do that due to numerical inaccuracies. So you should probably test for this case seperatelly.

The documentation for this class was generated from the following file:

csgeom/math3d.h