# Tools for tracing straight rays in Cartesian space {\RR^d}.
# Last edited on 2021-02-19 14:36:23 by jstolfi

import rootray_cart_IMP
import rootray

# See {rootray.py} for an explanation of root-rays.

# RAYTRACING PRIMITIVES

# In the procedure of this section, the trajectory {r} is defined by two
# points {p,q} of some Cartesian space {\RR^d}, as {r(t) = t p +
# (1-t)q}. Note that this trajectory spans the whole infinite straight
# line defined by the two points. Each procedure returns a root ray for
# {r} relative to some simple subset {F} of {\RR^n}. The two points must
# be distinct.
#
# The points must be tuples or lists of floats with the same length {d}.
# These shapes assume the Cartesian model of Euclidean space.
  
def halfspace(p, q, k):
  # The figure {F} is the halfspace whose interior is all points whose coordinate {k} 
  # is negative. The index{k} should be in {0..d-1}.
  return rootray_cart_IMP.halfspace(p, q, k)
  
def slab(p, q, k):
  # The figure {F} consists of the points whose coordinate {k} is in the range {(-1 _ +1)}.
  return rootray_cart_IMP.slab(p, q, k)

def ball(p, q):
  # The figure {F} is the {d}-dimensional ball of unit radius centered 
  # at the origin.
  return rootray_cart_IMP.ball(p, q)
  
def cube(p, q):
  # The figure {F} is the axis-aligned {d}-dimensional hypercube of side 
  # 2 centered at the origin; that is, {[-1 _+1]^d}.
  return rootray_cart_IMP.cube(p, q)
  
def cylinder(p, q, m):
  # The figure {F} is a cylinder centered at the origin
  # that is a ball of unit radius on the first {m} coordinates,
  # and unrestrited in the last {d-m}. For example, if {d=3} and {m=2}, then {F}
  # is the infinite cylinder in {\RR^3} radius 1 whose axis is the {Z} axis.
  #
  # If {m == 0}, this is equivalent to {plenum()}. If {m == 1}, this is equivalent to {slab(p,q,0)}.
  # If {m == d}, this is equivalent to {ball(p,q)}.
  return rootray_cart_IMP.cylinder(p, q, m)
  
def cone(p, q, m):
  # The figure {F} is the quadratic form of {\RR^d} which is the sum of squares
  # of the first {m} coordinates minus the sum of squares of the last {d-m}.
  #
  # For example, if {d=3} and {m=2}, {F} consists of the two oppositely directed infinite cones
  # with vertex at the origin and revolving around the {Z} axis, with walls sloping at 45 degrees.
  # If {d=2} and {m=1}, {F} is the 
  #
  # If {m == 0}, this is essentially equivalent to {plenum()}. If {m == d}, this is essentially
  # equivalent {vacuum}.  In general, {cone(p,q,m)} is the complement of {cone(p,q,d-m)}.
  # If {m == d}, this is equivalent to {ball(p,q)}.
  return rootray_cart_IMP.cone(p, q, m)