Path class, defines control points and a cubic Bezier approximation for defining a smooth path from key frames. More...

#include <path.hpp>

Inheritance diagram for Tucano::Path:

Public Member Functions
	Path ()
	Default constructor. More...

void	reset (void)
	Resets the path. More...

void	initOpenGLMatrices (void)
	Initializes the view and projection matrices. They are all initialized as Identity matrices, but view is then translated by the defaultTranslation vector. More...

void	initialize (string shader_dir="../effects/shaders/")
	Initializes shaders. More...

void	fillVertexData (void)
	Fill the vertices array. More...

void	addKeyPosition (const Tucano::Camera &camera, float interval=0.0)
	Add key position The camera will pause at this position for given number of steps, default is zero. More...

void	addKeyDirection (const Eigen::Quaternion< float > q)
	Add an optial key direction Key directions are interpolated via SLERP and not SQUAD This is specially useful for interpolating a light direction together with the camera path Key directions should be always allocated together with a key position to work properly. More...

void	render (const Tucano::Camera &camera, const Tucano::Camera &light)
	Renders smooth path End points for each Beziér is passed as line_strip and control points as vertex attributes Inside geometry shader each Beziér segment is approximate by linear segments. More...

int	curveSegment (float t)
	returns the segment given a time t in [0,1] for the whole path More...

float	toLocalParameter (float t)
	converts global parameter t to a local t inside a segment More...

Eigen::Vector4f	pointOnSegment (float t, int segment)
	Returns a point at time t on a given Beziér segment. More...

Eigen::Vector4f	pointOnPath (float global_t)
	compute point on path given t in [0,1] More...

Eigen::Quaternionf	logQuaternion (const Eigen::Quaternionf &qi)
	Returns the log of a quaternion log(q) q in the form [cos(a), sin(a) v], log(q) = [0, a v]. More...

Eigen::Quaternionf	expQuaternion (const Eigen::Quaternionf &q)
	Returns the exp of a quaternion exp(q) q in the form [0, a v], exp(q) = [cos(a), sin(a) v] with \|v\|=1. More...

Eigen::Quaternionf	squad (int seg, float t)
	SQUAD - Spherical and Quadrangle quaternion interpolation. More...

Eigen::Affine3f	cameraAtTime (float global_t)
	return a view matrix at a given path parameter More...

Eigen::Quaternion< float >	directionAtTime (float global_t)
	return a direction at a given path parameter More...

Eigen::Affine3f	cameraAtCurrentTime (void)
	Return the view matrix at current animation time. More...

Eigen::Quaternion< float >	directionAtCurrentTime (void)
	Return the direction at current animation time. More...

float	arcLengthToTime (float s)
	Converts from given arc length to time parameter. More...

void	toggleAnimation (void)
	Toggle animation. More...

void	setLoopAnimation (bool f)
	Set loop animation flag. More...

void	toggleDrawControlPoints (void)
	Toggle render control points. More...

void	toggleDrawQuaternions (void)
	Toggle render control quaternions. More...

bool	isAnimating (void)
	Returns if Animation is running or not. More...

void	stepForward (void)
	Move animation forward one step. More...

void	stepBackward (void)
	Move animation backward one step. More...

void	startAnimation (void)
	Start animation following camera path. More...

void	stopAnimation (void)
	Stop animation. More...

void	resetAnimation (void)
	Resets animation to first key position. More...

float	animTime (void)
	Return current animation time. More...

float	animSpeed (void)
	Return animation speed where 1 covers the whole curve in one step. More...

void	setAnimSpeed (float as)
	Sets the animation speed. More...

void	computeControlQuaternions (void)
	Compute control points for SQUAD. More...

void	computeInnerControlPoints (void)
	Compute inner control points from key positions. More...

void	computeArcLength (void)
	Compute an approximation of the arclength. More...

void	printDebugInfo (void)

void	writeToFile (const string filename)

void	loadFromFile (const string filename)

Public Member Functions inherited from Tucano::Camera
void	resetViewMatrix (void)
	Reset view matrix. More...

void	resetProjectionMatrix (void)
	Reset projection matrix. More...

void	reset (void)
	Resets trackball to initial position and orientation. More...

Eigen::Vector3f	getCenter (void) const
	Returns the center of the camera in world space. More...

void	getViewMatrix (GLdouble *matrix)
	Return the modelview matrix as a GLdouble array. More...

void	getProjectionMatrix (GLdouble *matrix)
	Return the projection matrix as a GLdouble array. More...

Eigen::Vector3f	projectPoint (const Eigen::Vector4f &pt, Eigen::Vector4f &viewport)
	Returns screen space coordinates of a 3D point. More...

Eigen::Affine3f	getViewMatrix (void) const
	Returns the view matrix as an Affine 3x3 matrix. More...

Eigen::Affine3f *	viewMatrix (void)
	Returns a pointer to the view matrix as an Affine 3x3 matrix. More...

Eigen::Matrix4f	getProjectionMatrix (void) const
	Returns the view matrix as an 4x4 matrix. More...

Eigen::Matrix4f *	projectionMatrix (void)
	Returns a pointer to the projection matrix as an 4x4 matrix. More...

Eigen::Matrix3f	getRotationMatrix (void) const
	Returns a 3x3 matrix containing only the rotation of the view matrix. More...

Eigen::Vector3f	getTranslationMatrix (void) const
	Returns the translation part of the view matrix as a vector. More...

float	getPerspectiveScale (void) const
	Returns the perspective scale. More...

Eigen::Vector4f	getViewport (void) const
	Returns the viewport coordinates. More...

Eigen::Vector2i	getViewportSize (void) const
	Returns the dimensions of the viewport. More...

float	getViewportAspectRatio (void) const
	Returns the viewport aspect ratio. More...

void	setViewport (const Eigen::Vector4f &vp)
	Sets the viewport coordinates. More...

void	setViewport (const Eigen::Vector2i &vp)

void	setViewport (const Eigen::Vector2f &vp)
	Sets the viewport coordinates considering that the minimum coordinates are zero. More...

void	setProjectionMatrix (const Eigen::Matrix4f &mat)
	Sets the projection matrix from a given 4x4 matrix. More...

void	setViewMatrix (const Eigen::Affine3f &mat)
	Sets the view matrix from a given an affine 3x3 matrix. More...

float	getNearPlane (void) const
	Returns near plane value. More...

float	getFarPlane (void) const
	Returns far plane value. More...

	~Camera ()
	Default destructor. More...

float	getFovy (void) const
	Returns current field of view angle in y axis. More...

	Camera (void)
	Default constructor. More...

Eigen::Matrix4f	setPerspectiveMatrix (float fy, float in_aspect_ratio, float in_near_plane, float in_far_plane)
	Sets the projection matrix as a perspective matrix. More...

void	changeFovy (float new_fovy)
	Changes the fovy and computes new perspective projection matrix. More...

Eigen::Matrix4f	setOrthographicMatrix (float left, float right, float bottom, float top, float near_plane, float far_plane)
	Sets the projection matrix as a orthographic matrix. More...

void	incrementFov (float inc)
	Increases the fov of the perspective matrix by a given increment. More...

void	translate (const Eigen::Vector3f &translation)
	Translates the view matrix by a given vector. More...

void	rotate (const Eigen::Quaternion< float > &rotation)
	Rotate the view matrix by a given quaternion. More...

void	scale (const Eigen::Vector3f &scale_factors)
	Scales the view matrix by given factors. More...

void	scale (float scale_factor)
	Scales the view matrix by given factor in all axis. More...

Private Attributes
float	anim_speed = 0.025
	Movement speed, arc length increment for each animation step. More...

float	anim_time = 0.0
	Animation time. More...

bool	animating = false
	Start/stop animation. More...

bool	loop_animation = false
	Flag to loop animation. More...

bool	draw_control_points = false
	Flag to render control points. More...

bool	draw_quaternions = false
	Flag to render quaternions at key positions. More...

vector< Eigen::Vector4f >	key_positions
	Camera position at each Key frames. More...

vector< float >	key_intervals
	Steps to stay paused at a given key position, usually zero. More...

vector< Eigen::Vector4f >	control_points_1
	First control point between two key positions. More...

vector< Eigen::Vector4f >	control_points_2
	Second control point between two key positions. More...

vector< vector< float > >	arc_lengths
	Arc-length approximation splitting each Beziér segment into linear segments. More...

float	path_length
	Total path length. More...

vector< Eigen::Quaternion< float > >	key_quaternions
	Rotation state at each key frame. More...

vector< Eigen::Quaternion< float > >	control_quaternions
	Control quaternions for SQUAD. More...

vector< Eigen::Quaternion< float > >	key_directions
	Rotation only interpolation (via Slerp) useful for accompaning light direction for example. More...

Mesh	curve

Mesh	control_segments

Shapes::Sphere	sphere
	A sphere to visually represent the path's key positions. More...

Shapes::CoordinateAxes	axes
	Coordinate axes for visualizing quaternions at key positions. More...

Shader	camerapath_shader
	Path shader, used for rendering the curve. More...

Shader	phong_shader
	To render simple lines. More...

Additional Inherited Members
Static Public Member Functions inherited from Tucano::Camera
static Eigen::Matrix4f	createPerspectiveMatrix (float fy, float in_aspect_ratio, float in_near_plane, float in_far_plane)
	Returns a perspective projection matrix with the given parameters. More...

static Eigen::Matrix4f	createOrthographicMatrix (float left, float right, float bottom, float top, float near_plane, float far_plane)
	Returns an orthographic projection matrix with the given parameters. More...

Protected Attributes inherited from Tucano::Camera
Eigen::Matrix4f	projection_matrix
	Projection, or intrinsic, matrix. More...

Eigen::Affine3f	view_matrix
	View, or extrinsic, matrix. More...

Eigen::Vector4f	viewport
	Viewport dimensions [minX, minY, width, height]. More...

Eigen::Affine3f	default_view

float	near_plane
	Near plane used for projection matrix. More...

float	far_plane
	Far plane used for projection matrix. More...

float	frustum_left
	Frustum left dimension. More...

float	frustum_right
	Frustum right dimension. More...

float	frustum_top
	Frustum top dimension. More...

float	frustum_bottom
	Frustum bottom dimension. More...

float	aspect_ratio
	Aspect ratio for projection matrix. More...

float	focal_length
	Camera's Focal Length. More...

float	fovy
	Field of view angle in y axis. More...

bool	use_perspective
	Flag to indicate if using a perspective or othograpic projection. More...

Detailed Description

Path class, defines control points and a cubic Bezier approximation for defining a smooth path from key frames.

Very useful for creating camera paths for example, but it is generic enough to be used for other purposes. Each key frame stores a position and an orientation.

Reference: https://www.particleincell.com/2012/bezier-splines/

Notation: We refer to time as the curve parameter (analogy to particle moving along path) We refer to curve as the whole path, and a segment as one Cubic Bezíér that composes path

Constructor & Destructor Documentation

Tucano::Path::Path ( )

inline

Default constructor.

Member Function Documentation

void Tucano::Path::addKeyDirection ( const Eigen::Quaternion< float > q )

inline

Add an optial key direction Key directions are interpolated via SLERP and not SQUAD This is specially useful for interpolating a light direction together with the camera path Key directions should be always allocated together with a key position to work properly.

Parameters

camera Camera with directional information

void Tucano::Path::addKeyPosition	(	const Tucano::Camera &	camera,
		float	interval = `0.0`
	)

inline

Add key position The camera will pause at this position for given number of steps, default is zero.

Parameters

camera	Camera containing position and orientation in view matrix
interval	Number of steps to stay at this position

float Tucano::Path::animSpeed ( void )

inline

Return animation speed where 1 covers the whole curve in one step.

Returns: Animation speed

float Tucano::Path::animTime ( void )

inline

Return current animation time.

Returns: anim time

float Tucano::Path::arcLengthToTime ( float s )

inline

Converts from given arc length to time parameter.

Parameters

s	Arc length parameter in [0,1]

Returns: Time at given arc length

Eigen::Affine3f Tucano::Path::cameraAtCurrentTime ( void )

inline

Return the view matrix at current animation time.

Returns: View matrix at current animation time

Eigen::Affine3f Tucano::Path::cameraAtTime ( float global_t )

inline

return a view matrix at a given path parameter

Returns: view matrix at time t of the path

void Tucano::Path::computeArcLength ( void )

inline

Compute an approximation of the arclength.

approximates the curve by linear segments divide the curve between two key positions and compute the total length of the linear segments

void Tucano::Path::computeControlQuaternions ( void )

inline

Compute control points for SQUAD.

Quaternions, Interpolation and Animation, Erik B. Dam, Martin Koch, Martin Lillholm

void Tucano::Path::computeInnerControlPoints ( void )

inline

Compute inner control points from key positions.

For each pair of subsequent key positions, compute two control points to define a Beziér Spline. Since we are restricting the splines to join with same position, and first two derivatives, the result is a smooth curve passing through all control points See reference at class info for more details.

To solve the tridiagonal system we use Thomas Algorithm (see Wikipedia)

int Tucano::Path::curveSegment ( float t )

inline

returns the segment given a time t in [0,1] for the whole path

Returns: curve segment number

Eigen::Quaternion<float> Tucano::Path::directionAtCurrentTime ( void )

inline

Return the direction at current animation time.

Returns: Interpolated direction as Quaternion at current animation time

Eigen::Quaternion<float> Tucano::Path::directionAtTime ( float global_t )

inline

return a direction at a given path parameter

Returns: quaternion with interpolated direction

Eigen::Quaternionf Tucano::Path::expQuaternion ( const Eigen::Quaternionf & q )

inline

Returns the exp of a quaternion exp(q) q in the form [0, a v], exp(q) = [cos(a), sin(a) v] with |v|=1.

Parameters

q	Given quaternion

Returns: exp(q)

void Tucano::Path::fillVertexData ( void )

inline

Fill the vertices array.

void Tucano::Path::initialize ( string shader_dir = "../effects/shaders/" )

inline

Initializes shaders.

Parameters

shader_dir Location of shader files

void Tucano::Path::initOpenGLMatrices ( void )

inline

Initializes the view and projection matrices. They are all initialized as Identity matrices, but view is then translated by the defaultTranslation vector.

bool Tucano::Path::isAnimating ( void )

inline

Returns if Animation is running or not.

Returns: True if animation is running, false otherwise

void Tucano::Path::loadFromFile ( const string filename )

inline

Eigen::Quaternionf Tucano::Path::logQuaternion ( const Eigen::Quaternionf & qi )

inline

Returns the log of a quaternion log(q) q in the form [cos(a), sin(a) v], log(q) = [0, a v].

Parameters

qi	Given quaternion

Returns: log(q)

Eigen::Vector4f Tucano::Path::pointOnPath ( float global_t )

inline

compute point on path given t in [0,1]

Note that t refers to the whole path, so t=0 is the first key position and t=1 is the last key position

Parameters

global_t Global parameter on path in [0,1]

Eigen::Vector4f Tucano::Path::pointOnSegment	(	float	t,
		int	segment
	)

inline

Returns a point at time t on a given Beziér segment.

Parameters

t	Beziér segment parameter
segment	Beziér segment on path

Returns: Point on curve

void Tucano::Path::printDebugInfo ( void )

inline

void Tucano::Path::render	(	const Tucano::Camera &	camera,
		const Tucano::Camera &	light
	)

inline

Renders smooth path End points for each Beziér is passed as line_strip and control points as vertex attributes Inside geometry shader each Beziér segment is approximate by linear segments.

Parameters

camera	Current camera for viewing scene
light	Camera representing light (position and orientation)

void Tucano::Path::reset ( void )

inline

Resets the path.

void Tucano::Path::resetAnimation ( void )

inline

Resets animation to first key position.

void Tucano::Path::setAnimSpeed ( float as )

inline

Sets the animation speed.

Parameters

as	Given animation speed

void Tucano::Path::setLoopAnimation ( bool f )

inline

Set loop animation flag.

Parameters

f	True for loop animation, false otherwise

Eigen::Quaternionf Tucano::Path::squad	(	int	seg,
		float	t
	)

inline

SQUAD - Spherical and Quadrangle quaternion interpolation.

Parameters

seg	The current Bezièr segment
t	Interpolatio time

void Tucano::Path::startAnimation ( void )

inline

Start animation following camera path.

void Tucano::Path::stepBackward ( void )

inline

Move animation backward one step.

void Tucano::Path::stepForward ( void )

inline

Move animation forward one step.

void Tucano::Path::stopAnimation ( void )

inline

Stop animation.

void Tucano::Path::toggleAnimation ( void )

inline

Toggle animation.

void Tucano::Path::toggleDrawControlPoints ( void )

inline

Toggle render control points.

void Tucano::Path::toggleDrawQuaternions ( void )

inline

Toggle render control quaternions.

float Tucano::Path::toLocalParameter ( float t )

inline

converts global parameter t to a local t inside a segment

Returns: Local parameter t in [0,1] for a single Cubic Beziér segment

void Tucano::Path::writeToFile ( const string filename )

inline

Member Data Documentation

float Tucano::Path::anim_speed = 0.025

private

Movement speed, arc length increment for each animation step.

float Tucano::Path::anim_time = 0.0

private

Animation time.

bool Tucano::Path::animating = false

private

Start/stop animation.

vector< vector <float> > Tucano::Path::arc_lengths

private

Arc-length approximation splitting each Beziér segment into linear segments.

Shapes::CoordinateAxes Tucano::Path::axes

private

Coordinate axes for visualizing quaternions at key positions.

Shader Tucano::Path::camerapath_shader

private

Path shader, used for rendering the curve.

vector< Eigen::Vector4f > Tucano::Path::control_points_1

private

First control point between two key positions.

vector< Eigen::Vector4f > Tucano::Path::control_points_2

private

Second control point between two key positions.

vector< Eigen::Quaternion<float> > Tucano::Path::control_quaternions

private

Control quaternions for SQUAD.

Mesh Tucano::Path::control_segments

private

Mesh Tucano::Path::curve

private

Mesh with path's key positions and computed control points for drawing smooth curve between key positions

bool Tucano::Path::draw_control_points = false

private

Flag to render control points.

bool Tucano::Path::draw_quaternions = false

private

Flag to render quaternions at key positions.

vector< Eigen::Quaternion<float> > Tucano::Path::key_directions

private

Rotation only interpolation (via Slerp) useful for accompaning light direction for example.

vector< float > Tucano::Path::key_intervals

private

Steps to stay paused at a given key position, usually zero.

vector< Eigen::Vector4f > Tucano::Path::key_positions

private

Camera position at each Key frames.

vector< Eigen::Quaternion<float> > Tucano::Path::key_quaternions

private

Rotation state at each key frame.

bool Tucano::Path::loop_animation = false

private

Flag to loop animation.

float Tucano::Path::path_length

private

Total path length.

Shader Tucano::Path::phong_shader

private

To render simple lines.

Shapes::Sphere Tucano::Path::sphere

private

A sphere to visually represent the path's key positions.

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

tucano/utils/path.hpp

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation