/*
 *	Dirichlet_rotate.c
 *
 *	This file provides the following functions for the UI, to allow
 *	convenient Dirichlet domain rotation.
 *
 *		void set_identity_matrix(O31Matrix position);
 *		void set_poly_velocity(O31Matrix velocity, double theta[3]);
 *		void update_poly_position(O31Matrix position, O31Matrix velocity);
 *		void update_poly_vertices(WEPolyhedron *polyhedron,
 *								O31Matrix position, double scale);
 *		void update_poly_visibility(WEPolyhedron *polyhedron,
 *								O31Matrix position, O31Vector direction);
 *
 *	set_identity_matrix() sets a position or velocity matrix to the identity.
 *
 *	set_poly_velocity() takes as input the small rotation angles theta[]
 *		about each of the coordinate axes, and computes the corresonding
 *		rotation matrix.  set_poly_velocity() may be used to update the
 *		velocity when the user drags the polyhedron with the mouse.
 *		For example, say the user interface is using a coordinate system
 *		in which the x-axis points to the right, the y-axis points down,
 *		and the z-axis points into the screen, and the user drags the
 *		mouse a small distance (dx, dy).  The dx corresponds to a small
 *		clockwise rotation about the y-axis.  The dy corresponds to a small
 *		counterclockwise rotation about the x-axis.  So we pass the vector
 *		theta[3] = (dy, -dx, 0) to set_poly_velocity() and get back the
 *		corresponding velocity matrix.
 *
 *	update_poly_position() updates the position by left-multiplying by the
 *		velocity.  Call it to keep the polyhedron moving.
 *
 *	update_poly_vertices() multiplies the standard vertex coordinates x[]
 *		by the position matrix to obtain the rotated coordinates xx[].
 *		It then multiplies the rotated coordinates by the constant "scale";
 *		this lets the UI scale the rotated coordinates to match the window
 *		coordinates (if you don't need this feature, pass scale = 1.0).
 *
 *	update_poly_visibility() checks which vertices, edges and faces are
 *		visible to the user with the polyhedron in its present position,
 *		and sets their visibility fields accordingly.  The direction vector
 *		points from the center of the polyhedron to the user.  Note that
 *		the direction vector is an O31Vector;  just set the 0-th component
 *		to 0.0.
 */

#include "kernel.h"

static void	set_face_visibility(WEPolyhedron *polyhedron, O31Matrix position, O31Vector direction);
static void	set_edge_visibility(WEPolyhedron *polyhedron);
static void	set_vertex_visibility(WEPolyhedron *polyhedron);


void set_identity_matrix(
	O31Matrix	m)
{
	/*
	 *	This function is just a wrapper around a call to
	 *	o31_copy(position, O31_identity), to avoid giving
	 *	the UI access to the kernel's O(3,1) matrix library.
	 */

	o31_copy(m, O31_identity);
}


void update_poly_position(
	O31Matrix	position,
	O31Matrix	velocity)
{
	/*
	 *	Multiply the position by the velocity to get the new position.
	 */

	o31_product(velocity, position, position);
}


void update_poly_vertices(
	WEPolyhedron	*polyhedron,
	O31Matrix		position,
	double			scale)
{
	WEVertex	*vertex;

	for (vertex = polyhedron->vertex_list_begin.next;
		 vertex != &polyhedron->vertex_list_end;
		 vertex = vertex->next)
	{
		o31_matrix_times_vector(position, vertex->x, vertex->xx);
		o31_constant_times_vector(scale, vertex->xx, vertex->xx);
	}
}


void update_poly_visibility(
	WEPolyhedron	*polyhedron,
	O31Matrix		position,
	O31Vector		direction)
{
	/*
	 *	Check which vertices, edges and faces are visible to the user with
	 *	the polyhedron in its present position, and set their visibility
	 *	fields accordingly.  The direction vector points from the center
	 *	of the polyhedron to the user.
	 */

	/*
	 *	direction[0] is probably zero already, but just in case it's not,
	 *	set it to zero explicitly.  (We're using O31Vectors, but we care
	 *	only about the 3-dimensional part.)
	 */
	direction[0] = 0.0;

	/*
	 *	Set the face visibility first.
	 */
	set_face_visibility(polyhedron, position, direction);

	/*
	 *	An edge is visible iff it lies on a visible face.
	 */
	set_edge_visibility(polyhedron);

	/*
	 *	A vertex is visible iff it lies on a visible edge.
	 */
	set_vertex_visibility(polyhedron);
}


static void set_face_visibility(
	WEPolyhedron	*polyhedron,
	O31Matrix		position,
	O31Vector		direction)
{
	WEFace		*face;
	O31Vector	old_normal,
				new_normal;
	int			i;

	for (face = polyhedron->face_list_begin.next;
		 face != &polyhedron->face_list_end;
		 face = face->next)
	{
		/*
		 *	The first column of the group_element provides a normal
		 *	vector relative to the polyhedron's original position.
		 */
		for (i = 0; i < 4; i++)
			old_normal[i] = (*face->group_element)[i][0];

		/*
		 *	Apply the position matrix to find the normal vector relative
		 *	to the polyhedron's current position.
		 */
		o31_matrix_times_vector(position, old_normal, new_normal);

		/*
		 *	The face will be visible iff the new_normal has a positive
		 *	component in the given direction.
		 */
		face->visible = (o31_inner_product(direction, new_normal) > 0.0);
	}
}


static void set_edge_visibility(
	WEPolyhedron	*polyhedron)
{
	WEEdge	*edge;

	for (edge = polyhedron->edge_list_begin.next;
		 edge != &polyhedron->edge_list_end;
		 edge = edge->next)

		edge->visible = (edge->f[left]->visible || edge->f[right]->visible);
}


static void set_vertex_visibility(
	WEPolyhedron	*polyhedron)
{
	WEVertex	*vertex;
	WEEdge		*edge;

	/*
	 *	Initialize all vertex visibilities to FALSE.
	 */

	for (vertex = polyhedron->vertex_list_begin.next;
		 vertex != &polyhedron->vertex_list_end;
		 vertex = vertex->next)

		vertex->visible = FALSE;

	/*
	 *	The endpoints of each visible edge will be visible vertices.
	 */

	for (edge = polyhedron->edge_list_begin.next;
		 edge != &polyhedron->edge_list_end;
		 edge = edge->next)

		if (edge->visible)
		{
			edge->v[tail]->visible	= TRUE;
			edge->v[tip ]->visible	= TRUE;
		}
}