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spline(spline) Spline Interpolation spline(spline)

NAME

spline - spline superclass

SUPERCLASS

object

DESCRIPTION

Spline is used to create interpolated data points for specified data. Spline is a mixin object and is not instantiated by itself, rather as instances of its subclasses c_spline, k_spline, o_spline, and q_spline. Interpolation is done by these specific classes. Spline object has instance variables and responds to messages common to all its subclasses. The current implementation of spline is limited to data dimension not exceeding four.

INSTANCE VARIABLES

end is the value of the right boundary of independent variable for spline evaluation.

data is the name of the data object associated with the spline.

duration is the difference between end and start values of an instance.

left_code is the type of constraint at left most point. Left_value depends on left_constraint: left_code= 1 -> first derivative = left_value left_code= 2 -> second derivative = left_value left_code= 3 -> second derivative = left_value * second derivative of first interior point.

left_value is the variable for specifying the left most point derivative (see left_code).

min is the minimum value of the spline.

max is the maximum value of the spline.

normalize_time is the indicator whether time considered to be normalized or not. If it is 1 then normalization of time is performed based on start and end values.

old_values is the spline interpolated data at previous tick.

open is an indicator whether spline is considered open or closed.

resolution is the number of ticks (frames) per second. For each tick time is incremented by 1/resolution.

right_code is the type of constraint at right most point. Right_value depends on right_constraint: right_value= 1 -> first derivative = right_value right_value= 2 -> second derivative = right_value right_value= 3 -> second derivative = right_value * second derivative of last interior point.

right_value is the variable for specifying the right most point derivative (see left_code).

truncate is the flag to truncate the spline value to min and max.

scale is the flag for computed value to be scaled by max- min and add min.

start is the value of the left boundary of independent variable for spline evaluation.

time is the value of independent variable in the spline.

time_spline is the name of the time spline associated with a spline.

MESSAGES

data= argument Set the value of the data.

data? Return the value of the data.

duration= argument Set the value of the duration; end is recalculated as well.

duration+ argument Adds argument to the duration; end is recalculated as well.

duration? Return the value of the duration.

end+ argument Add the value of the end; duration is recalculated as well.

end= argument Set the value of the end; duration is recalculated as well.

end? Return the value of the end.

free! Free instance storage and remove it from the object table.

left_acceleration= argument Set the left_value of the spline to the argument and the left_code to 2.

left_code= argument Set the value of the left_code.

left_code? Return the value of the left_code.

left_value= argument Set the value of the left_value.

left_value? Return the value of the left_value.

left_velocity= argument Set the left_value of the spline to the argument and the left_code to 1.

max= argument Set the max of the spline to the argument.

max? Return the max of the spline.

min= argument Set the min of the spline to the argument.

min? Return the min of the spline.

normalize_time= argument Set the normalize_time flag to the argument. One is to normalize time and 0 to do not normalization.

normalize_time? Return normalize_time flag.

normalize_time_off! Set normalize_time flag to OFF (0).

normalize_time_on! Set normalize_time flag to ON (1).

old_values= argument Set the value of old_values variable.

old_values? Return the value of old_values variable.

open= argument Set the open flag of the spline.

open? Return the open flag of the spline.

open_off! Set the open flag to OFF (0).

open_on! Set the open flag to ON (1).

resolution= argument Set the resolution of the spline.

resolution? Return the resolution of the spline.

results? Returns the result of interpolating the spline from its current time to its end by repeatedly sending tick! messages until the time exceeds the end. The time instance variable is modified by this procedure.

right_acceleration= argument Set the right_value of the spline to the argument and the right_code to 2.

right_code= argument Set the right_code of the spline to the argument.

right_code? Return the right_code value.

right_value= argument Set the right_value of the spline.

right_value? Return the right value.

right_velocity= argument Set the right_value of the spline to the argument and the right_code to 1.

scale= argument Set the scale flag of the spline to the argument.

scale? return the scale flag.

scale_off! Set the scale flag OFF (0).

scale_on! Set the scale flag ON (1).

start+ argument Add the start of the spline and recalculate the duration.

start= argument Set the start of the spline and recalculate the duration.

start? Return the start value of the spline.

time+ argument Add time value of the spline.

time= argument Set time value of the spline.

time? Return time value of the spline.

time_spline= argument Set the time_spline value of the spline.

time_spline? Return the time_spline value of the spline.

truncate= argument Set the truncate flag of the spline.

truncate? Return the truncate flag of the spline.

truncate_off! Set the truncate flag of the spline to OFF (0).

truncate_on! Set the truncate flag of the spline to ON (1).

EXAMPLE

Spline object is used in combination with data object. Splines are usually used to calculate intermediate values for various parameters in animation. As a rule, complicated scripts for splines are generated automatically by various generator objects (camera_generator, actor_generator, keyframe).

Below is slightly abbreviated script generated by keyframe object.

This script assumes that camera c1 is defined and there is an actor, a

modeller, a scene, and a renderer. The script controlls animation of a

camera orientation. */

cue new: key1_c1_azimuth; k_spline new: key1_c1_azimuth_spline; data new: key1_c1_azimuth_data dimension= 1;

key1_c1_azimuth_data t= 0.000000 value= 0.000000; key1_c1_azimuth_data t= 1.000000 value= -5.000000; key1_c1_azimuth_data t= 2.000000 value= 5.000000; key1_c1_azimuth_data t= 3.000000 value= 0.000000; key1_c1_azimuth_data normalize_t!; key1_c1_azimuth_spline scale_off! max= 5.000000 min= -5.000000 duration= 3.000000 data= key1_c1_azimuth_data; key1_c1_azimuth start= 0.000000 end= 3.000000 start_actions+ "key1_c1_azimuth_spline time= 0;" tick_actions+ "c1 azimuth: [key1_c1_azimuth_spline delta!];" end_actions+ "key1_c1_azimuth_spline time= [key1_c1_azimuth_spline end?];" end_actions+ "c1 azimuth: [key1_c1_azimuth_spline delta!];";