diguyMathHelper Class Reference

Contains useful math functions. More...

#include <diguyMathHelper.h>

Public Member Functions
	diguyMathHelper ()
	~diguyMathHelper ()

Static Public Member Functions
General Functions
Unless otherwise specified, all functions callable from: C++ Script
static int	get_ballistic_arc_velocity (float delta_x, float delta_y, float delta_z, float initial_speed, float max_elevation, float min_elevation, float **\returnet_vel_x, float *ret_vel_y, float *ret_vel_z, float *ret_delta_x, float *ret_delta_y, float *ret_delta_z)
	Helper function to determine if a ballistic weapon (e.g. More...
static int	quadratic_formula (float a, float b, float c, float **\returnet1, float *ret2)
	Helper function to solve the quadratic equation (http://en.wikipedia.org/wiki/Quadratic_formula) or to report that there is no solution. More...
static int	calculate_euler_angles_from_vector (float x, float y, float z, float roll, float *yaw, float *pitch)
	Given a vector and a roll value, calculate the Euler angles of yaw and pitch. More...
static void	calculate_vector_from_euler_angles (float yaw, float pitch, float **\note, float *y, float *z)
	Given a vector and a roll value, calculate the Euler angles of yaw and pitch. More...
static float	calculate_slide_in_rate (float current_distance, float base_rate, float base_distance, float acceptable_remainder=0.0f)
	A helper function for when there is an object approaching a target, and the goal is for it to slow down in a realistic-looking way. More...
static float	exponential_formula (float c, float k, float t)
	Calculates the value of the exponential formula at time t. More...
static float	calculate_exponential_growth_constant (float relative_value, float t)
	Calculates the value of k for the exponential growth/decay formula. More...
static void	rotate_vector (float in_x, float in_y, float in_z, float rz, float rx, float ry, float *out_x, float *out_y, float *out_z)
	Rotate a vector by the given Euler angles. More...
static void	unrotate_vector (float in_x, float in_y, float in_z, float rz, float rx, float ry, float *out_x, float *out_y, float *out_z)
	Rotate a vector by the inverse of the orientation defined by three Euler angles. More...

Detailed Description

Contains useful math functions.

This class is meant to be home to general purpose math formula. Aside from the usefulness of the functions themselves, a secondary goal is to educate the user.

Constructor & Destructor Documentation

diguyMathHelper::diguyMathHelper

(

)

diguyMathHelper::~diguyMathHelper

(

)

Member Function Documentation

static int diguyMathHelper::get_ballistic_arc_velocity ( float  delta_x, float  delta_y, float  delta_z, float  initial_speed, float  max_elevation, float  min_elevation, float **\  returnet_vel_x, float *  ret_vel_y, float *  ret_vel_z, float *  ret_delta_x, float *  ret_delta_y, float *  ret_delta_z  )

static

Helper function to determine if a ballistic weapon (e.g.

artillery) can hit its target, given a target point, projectile speed, max and min elevation. If the designated target can't be hit (too close or far), this function will offer the closest possible point that can be hit.

Parameters

delta_x,delta_y,delta_z	position of target relative to start point
initial_speed	how fast the projectile is going out of the barrel
max_elevation	the maximum elevation of the weapon above horizontal
min_elevation	the minimum elevation of the weapon above horizontal
ret_vel_x,ret_vel_y,ret_vel_z	output parameters; the velocity the projectile must have
ret_delta_x,ret_delta_y,ret_delta_z	output parameters; the relative pos of point that will be hit (if preferred target can't be reached)

Returns:

1 on success, 0 on failure (float * arguments converted to return values in Lua)

static int diguyMathHelper::quadratic_formula ( float  a, float  b, float  c, float **\  returnet1, float *  ret2  )

static

Helper function to solve the quadratic equation (http://en.wikipedia.org/wiki/Quadratic_formula) or to report that there is no solution.

Parameters

a,b,c	see link above
ret1,ret2	output parameters; the solutions, if any exist

Returns:

1 if there's a solution; 0 otherwise (float * arguments converted to return values in Lua)

static int diguyMathHelper::calculate_euler_angles_from_vector ( float  x, float  y, float  z, float  roll, float *  yaw, float *  pitch  )

static

Given a vector and a roll value, calculate the Euler angles of yaw and pitch.

Parameters

x,y,z	the vector
roll	roll in degrees, clockwise is positive direction
yaw,pitch	return parameters, degrees

Returns:

1 if results are valid; 0 otherwise (float * arguments converted to return values in Lua)

static void diguyMathHelper::calculate_vector_from_euler_angles ( float  yaw, float  pitch, float **\  note, float *  y, float *  z  )

static

Given a vector and a roll value, calculate the Euler angles of yaw and pitch.

Parameters

x,y,z	the vector
roll	roll in degrees, clockwise is positive direction
yaw,pitch	return parameters, degrees

Returns:

1 if results are valid; 0 otherwise (float * arguments converted to return values in Lua)

static float diguyMathHelper::calculate_slide_in_rate ( float  current_distance, float  base_rate, float  base_distance, float  acceptable_remainder = 0.0f  )

static

A helper function for when there is an object approaching a target, and the goal is for it to slow down in a realistic-looking way.

If the object is infinitely far away from the target, the returned slide-in rate will be infinite (in theory, not practice, obviously). If the object is at the base distance, the slide-in rate will be the base rate. If the object is closer than that, the slide-in rate will approach zero.

Parameters

current_distance	distance to target (can be distance in the conventional sense, or any kind of quantity)
base_rate	the base rate of travel, per second, in the same units
base_distance	the exact distance at which the base rate applies
acceptable_remainder	how much distance can be left for the target to have been "reached"

Returns:

The new rate to assign to the object

Usage Notes:

• If current_distance is negative, it will simply be assumed that the object is on the other side of the target. Thus, the returned rate will be negative.
• One can easily apply a cap to the rate returned, so it's not too high
• To find time to decel from base rate, use t = 2 * base_distance / base_rate
• If we want to calculate a slide-OUT rate, use distance from starting point, rather than to target
• This function can even be used to calculate a deceleration value, if the "distances" are deltas between two speed values, and the base rate is the base deceleration value

static float diguyMathHelper::exponential_formula ( float  c, float  k, float  t  )

static

Calculates the value of the exponential formula at time t.

The formula is: y = c * e ^ (k * t) Its derivative is: y' = k * c * e ^ (k * t) = k * y

Calculating k:

ln(y) = ln(c) + k * t k = (ln(y) - ln(c)) / t to grow/decay to y1 in t = 1, c = 1: k = ln(y1)

Parameters

c	the starting quantity at time 0
k	the constant, positive for growth, negative for decay
t	time

Returns:

The value of the formula at given time

static float diguyMathHelper::calculate_exponential_growth_constant ( float  relative_value, float  t  )

static

Calculates the value of k for the exponential growth/decay formula.

Parameters

multiplier	a value relative to starting value (>1 for growth, <1 for decay)
t	number of seconds it takes for exponential formula to reach that multiple

Returns:

Value of k

static void diguyMathHelper::rotate_vector ( float  in_x, float  in_y, float  in_z, float  rz, float  rx, float  ry, float *  out_x, float *  out_y, float *  out_z  )

static

Rotate a vector by the given Euler angles.

x, y, z of vector to be rotated rx, ry, rz degrees to rotate by result x, y, z

Returns:

(float * arguments converted to return values in Lua)

static void diguyMathHelper::unrotate_vector ( float  in_x, float  in_y, float  in_z, float  rz, float  rx, float  ry, float *  out_x, float *  out_y, float *  out_z  )

static

Rotate a vector by the inverse of the orientation defined by three Euler angles.

x, y, z of vector to be rotated rx, ry, rz degrees to rotate by result x, y, z

Returns:

(float * arguments converted to return values in Lua)

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

• diguyMathHelper.h