Reference for current diffraction implementation

[jeertmans]

Hello, when reading your source code, I do not fully understand how you find the interaction point for diffraction. More precisely, this part of the code is a bit cryptic to me.
Do you have any reference explaining where this algorithm or method originates from?

Thank you in advance!

sionna/sionna/rt/solver_paths.py

Lines 2368 to 2437 in f5ea373

	# Quantites required for the computation of the interaction points
	# [1, num_sources, max_num_paths]
	a = dot(u_t,e_hat)
	# [num_targets, 1, max_num_paths]
	b = dot(u_r, e_hat)
	# [1, num_sources, max_num_paths]
	c = dot(u_t, u_t)
	# [num_targets, 1, max_num_paths]
	d = dot(u_r, u_r)
	# Quantites required for the computation of the interaction points
	# [num_targets, num_sources, max_num_paths]
	alpha = -tf.square(a) + tf.square(b) + c - d
	beta = 2.*(a*tf.square(b) - b*tf.square(a) + b*c - a*d)
	gamma = tf.square(b)*c - tf.square(a)*d
	# Normalized quantites to improve numerical preicion, only valid if
	# alpha != 0
	# [num_targets, num_sources, max_num_paths]
	beta_norm = tf.math.divide_no_nan(beta, alpha)
	gamma_norm = tf.math.divide_no_nan(gamma, alpha)
	delta = tf.square(beta_norm) - 4.*gamma_norm
	# Because of numerical imprecision, delta could be slighlty smaller than
	# 0
	# [num_targets, num_sources, max_num_paths]
	delta = tf.where(tf.less(delta, tf.zeros_like(delta)),
	tf.zeros_like(delta), delta)
	# Four possible outcomes depending on the value of the previous
	# quantities.
	# Values of t that minimizes the path length for each outcome.
	# [num_targets, num_sources, max_num_paths]
	t_min_1 = -a
	t_min_2 = -tf.math.divide_no_nan(gamma, beta)
	t_min_3 = (-beta_norm + tf.sqrt(delta))*0.5
	t_min_4 = (-beta_norm - tf.sqrt(delta))*0.5
	# Condition for each outcome to be selected
	# If a == b and c == d, then set to t_min_1
	# [num_targets, num_sources, max_num_paths]
	cond_1 = tf.logical_and(tf.experimental.numpy.isclose(a, b),
	tf.experimental.numpy.isclose(c, d))
	# If cond_1 does not hold and alpha == 0, then set to t_min_2
	# [num_targets, num_sources, max_num_paths]
	cond_2 = tf.logical_and(tf.logical_not(cond_1),
	tf.experimental.numpy.isclose(alpha,
	tf.zeros_like(alpha)))
	# If neither cond_1 nor cond_2 holds, then set to t_min_3 or t_min_4
	# depending on the signs of t+a and t+b
	# [num_targets, num_sources, max_num_paths]
	not_cond_12 = tf.logical_and(tf.logical_not(cond_1),
	tf.logical_not(cond_2))
	# [num_targets, num_sources, max_num_paths]
	t_min_3a = t_min_3 + a
	t_min_3b = t_min_3 + b
	# [num_targets, num_sources, max_num_paths]
	cond_3 = tf.logical_and(not_cond_12,
	tf.less_equal(tf.sign(t_min_3a)*tf.sign(t_min_3b), 0.0))
	# If none of conditions 1, 2, or 3 are satisfied, then all is left is
	# t_min_4
	# [num_targets, num_sources, max_num_paths]
	cond_4 = tf.logical_and(not_cond_12, tf.logical_not(cond_3))
	# Assign t_min according to the previously computed conditions
	# [num_targets, num_sources, max_num_paths]
	t_min = tf.zeros_like(cond_1, tf.float64)
	t_min = tf.where(cond_1, t_min_1, t_min)
	t_min = tf.where(cond_2, t_min_2, t_min)
	t_min = tf.where(cond_3, t_min_3, t_min)
	t_min = tf.where(cond_4, t_min_4, t_min)

[faycalaa]

Hello,

We are in the process of developing comprehensive documentation for the path tracing algorithms. However, it's important to note that this will require some time to complete.

[jeertmans]

Hello, no problems, thank you for your answer and for this great tool!

[gauravduggal]

The location of the diffraction point can be computed using the diffraction law or fermat's principle of least time. This paper has the related math: https://ieeexplore.ieee.org/abstract/document/10879253