Triangles in 3D space
PhilipRBrenan@yahoo.com, 2004, Perl License
Example t/triangle.t
#_ Triangle ___________________________________________________________ # Test 3d triangles # philiprbrenan@yahoo.com, 2004, Perl License #______________________________________________________________________ use Math::Zap::Vector; use Math::Zap::Vector2; use Math::Zap::Triangle; use Test::Simple tests=>25; $t = triangle (vector( 0, 0, 0), vector( 0, 0, 4), vector( 4, 0, 0), ); $u = triangle (vector( 0, 0, 0), vector( 0, 1, 4), vector( 4, 1, 0), ); $T = triangle (vector( 0, 1, 0), vector( 0, 1, 1), vector( 1, 1, 0), ); $c = vector(1, 1, 1); #_ Triangle ___________________________________________________________ # Distance to plane #______________________________________________________________________ ok($t->distance($c) == 1, 'Distance to plane'); ok($T->distance($c) == 0, 'Distance to plane'); ok($t->distance(2*$c) == 2, 'Distance to plane'); ok($t->distanceToPlaneAlongLine(vector(0,-1,0), vector(0,1,0)) == 1, 'Distance to plane towards a point'); ok($T->distanceToPlaneAlongLine(vector(0,-1,0), vector(0,1,0)) == 2, 'Distance to plane towards a point'); #_ Triangle ___________________________________________________________ # Permute the points of a triangle #______________________________________________________________________ ok($t->permute == $t, 'Permute 1'); ok($t->permute->permute == $t, 'Permute 2'); ok($t->permute->permute->permute == $t, 'Permute 3'); #_ Triangle ___________________________________________________________ # Intersection of a line with a plane defined by a triangle #______________________________________________________________________ #ok($t->intersection($c, vector(1, -1, 1)) == vector(1, 0, 1), 'Intersection of line with plane'); #ok($t->intersection($c, vector(-1, -1, -1)) == vector(0, 0, 0), 'Intersection of line with plane'); #_ Triangle ___________________________________________________________ # Test whether a point is in front or behind a plane relative to another # point #______________________________________________________________________ ok($t->frontInBehind($c, vector(1, 0.5, 1)) == +1, 'Front'); ok($t->frontInBehind($c, vector(1, 0, 1)) == 0, 'In'); ok($t->frontInBehind($c, vector(1, -0.5, 1)) == -1, 'Behind'); #_ Triangle ___________________________________________________________ # Parallel #______________________________________________________________________ ok($t->parallel($T) == 1, 'Parallel'); ok($t->parallel($u) == 0, 'Not Parallel'); #_ Triangle ___________________________________________________________ # Coplanar #______________________________________________________________________ #ok($t->coplanar($t) == 1, 'Coplanar'); #ok($t->coplanar($u) == 0, 'Not coplanar'); #ok($t->coplanar($T) == 0, 'Not coplanar'); #_ Triangle ___________________________________________________________ # Project one triangle onto another #______________________________________________________________________ $p = vector(0, 2, 0); $s = $t->project($T, $p); ok($s == triangle (vector(0, 0, 2), vector(0.5, 0, 2), vector(0, 0.5, 2), ), 'Projection of corner 3'); #_ Triangle ___________________________________________________________ # Convert space to plane coordinates and vice versa #______________________________________________________________________ ok($t->convertSpaceToPlane(vector(2, 2, 2)) == vector(0.5,0.5,2), 'Space to Plane'); ok($t->convertPlaneToSpace(vector2(0.5, 0.5)) == vector(2, 0, 2), 'Plane to Space'); #_ Triangle ___________________________________________________________ # Divide #______________________________________________________________________ $it = triangle # Intersects t (vector( 0, -1, 2), vector( 0, 2, 2), vector( 3, 2, 2), ); @d = $t->divide($it); ok($d[0] == triangle(vector(0, -1, 2), vector(0, 0, 2), vector(1, 0, 2))); ok($d[1] == triangle(vector(0, 2, 2), vector(0, 0, 2), vector(1, 0, 2))); ok($d[2] == triangle(vector(0, 2, 2), vector(1, 0, 2), vector(3, 2, 2))); $it = triangle # Intersects t (vector( 3, 2, 2), vector( 0, 2, 2), vector( 0, -1, 2), ); @d = $t->divide($it); ok($d[0] == triangle(vector(0, -1, 2), vector(0, 0, 2), vector(1, 0, 2))); ok($d[1] == triangle(vector(3, 2, 2), vector(1, 0, 2), vector(0, 0, 2))); ok($d[2] == triangle(vector(3, 2, 2), vector(0, 0, 2), vector(0, 2, 2))); $it = triangle # Intersects t (vector( 3, 2, 2), vector( 0, -1, 2), vector( 0, 2, 2), ); @d = $t->divide($it); ok($d[0] == triangle(vector(0, -1, 2), vector(1, 0, 2), vector(0, 0, 2))); ok($d[1] == triangle(vector(3, 2, 2), vector(1, 0, 2), vector(0, 0, 2))); ok($d[2] == triangle(vector(3, 2, 2), vector(0, 0, 2), vector(0, 2, 2)));
Definitions:
Space coordinates = 3d space
Plane coordinates = a triangle in 3d space defines a 2d plane with a natural coordinate system: the origin is the first point of the triangle, the (x,y) units of this plane are the sides from the triangles first point to its other points.
Create a triangle from 3 vectors specifying the coordinates of each corner in space coordinates.
Create a triangle from 3 vectors specifying the coordinates of each corner in space coordinates - synonym for "new".
Narrow (colinear) triangle?
Check its a triangle
Test its a triangle
Components of a triangle
Create a triangle from another triangle
Cyclically permute the points of a triangle
Center
Add a vector to a triangle
Subtract a vector from a triangle
Print triangle
# Get/Set accuracy for comparisons
Shortest distance from plane defined by triangle t to point p
Intersect line between two points with plane defined by triangle and return the intersection in plane coordinates. Identical logic as per intersection(). Note: no checks (yet) for line parallel to plane.
Distance to plane defined by triangle t going from a to b, or undef if the line is parallel to the plane
Convert space to plane coordinates
Convert splane to space coordinates
Determine whether a test point b as viewed from a view point a is in front of(1), in(0), or behind(-1) a plane defined by a triangle t. Identical logic as per intersection(), except this time we use the z component to determine the relative position of the point b. Note: no checks (yet) for line parallel to plane.
Are two triangle parallel? I.e. do they define planes that are parallel? If they are parallel, their normals will have zero cross product
Divide triangle b by a: split b into triangles each of which is not intersected by a. Triangles are easy to draw in 3d except when they intersect: If they do not intersect, we can always draw one on top of the other and obtain the correct result; If they do intersect, they have to be split along the line of intersection into a sub triangle and a quadralateral: which can be be split again to obtain a result consisting of only triangles. The splitting can be done once: Each new view point only requires the correct ordering of the non intersecting triangles.
Project onto the plane defined by triangle t the image of a triangle triangle T as viewed from a view point p. Return the coordinates of the projection of T onto t using the plane coordinates induced by t. The projection coordinates are (of course) 2d in the projection plane, however they are returned as the x,y components of a 3d vector with the z component set to the multiple of the distance from the view point to the corresponding corner of T required to reach t. If z > 1, this corner of T is in front the plane of t, if z < 1 this corner of T is behind the plane of t. The logic is the same as intersection().
Split a triangle into 4 sub triangles unless the sub triangles would be too small
Triangulate
Compare two triangles for equality
Operator overloads
Add operator.
Subtract operator.
Equals operator.
Print a triangle
Export "triangle"
philiprbrenan@yahoo.com
philiprbrenan@yahoo.com, 2004
Perl License.
To install Math::Zap::Draw, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::Zap::Draw
CPAN shell
perl -MCPAN -e shell install Math::Zap::Draw
For more information on module installation, please visit the detailed CPAN module installation guide.