import mitsuba as mi from mitsuba import Float, Bool from .special import * from ..utils import * from ..utils.helpers import * def sample_cosk_direction(sample, direction, k : Float = Float(2)): #k>2 # sample symmetrically w.r.t. the direction with cos(theta / k) right_sphere = sample >= 0.5 sample = dr.select(right_sphere, 2 * sample - 1, 2 * sample) angle_shift = k * dr.asin(sample * dr.sin(dr.pi /k)) angle_shift = dr.select(right_sphere, angle_shift, -angle_shift) angle_initial = dr.atan2(direction[1], direction[0]) angle = angle_initial + angle_shift sampled_direction = mi.Point2f(dr.cos(angle), dr.sin(angle)) pdf = dr.rcp(2 * k * dr.sin(dr.pi /k)) * dr.cos(angle_shift / k) return sampled_direction, pdf def pdf_cosk_direction(sampled_direction, direction, k): #k>2 angle_diff = dr.abs(dr.acos(dr.dot(sampled_direction, direction))) return dr.rcp(2 * k * dr.sin(dr.pi /k)) * dr.cos(angle_diff / k) @dr.syntax def sample_star_direction(sample, half_space_mask : Bool, boundary_normal : mi.Point2f) -> tuple[mi.Point2f, mi.Float]: angle = mi.Float(0) direction = mi.Point2f(0) pdf = mi.Float(0) if half_space_mask: angle = mi.Float((sample - 0.5) * dr.pi) direction = mi.Point2f(dr.sin(angle), dr.cos(angle)) direction = dr.normalize(to_world_direction(direction, boundary_normal)) pdf = Float(1/dr.pi) else: angle = mi.Float(2 * dr.pi * sample) direction = mi.Point2f(dr.sin(angle), dr.cos(angle)) pdf = Float(1 / (2 * dr.pi)) return direction, pdf def sample_uniform_direction(sample): theta = 2 * dr.pi * sample return mi.Point2f(dr.sin(theta), dr.cos(theta)), Float(1/(2 * dr.pi)) def sample_uniform_boundary(sample, origin, radius): direction, pdf = sample_uniform_direction(sample) sampled_points = origin + radius * direction return sampled_points, pdf / radius def sample_cosine_direction(sample : Float, direction : mi.Point2f) -> tuple[mi.Point2f, Float, Float]: upper_sphere = sample >= 0.5 sample = dr.select(upper_sphere, 2 * sample - 1, 2 * sample) angle_shift = dr.asin(2 * sample - 1) abs_dot_prod = dr.sqrt(1 - dr.square(2 * sample -1)) angle_initial = dr.atan2(direction[1], direction[0]) angle = angle_initial + angle_shift sampled_direction = mi.Point2f(dr.cos(angle), dr.sin(angle)) sign = dr.select(upper_sphere, Float(1), Float(-1)) sampled_direction *= sign return sampled_direction, abs_dot_prod / 4, sign def sample_cosine_boundary(sample : Float, origin : mi.Point2f, radius : Float, direction : mi.Point2f) -> tuple[mi.Point2f, Float, Float]: sampled_direction, pdf, sign = sample_cosine_direction(sample, direction) point = origin + radius * sampled_direction return point, pdf / radius, sign def sample_cosine_boundary_antithetic(sample, origin, radius, direction, active): angle_shift = dr.asin(2 * sample - 1) direction1 = mi.Point2f(dr.sin(angle_shift), dr.cos(angle_shift)) direction2 = mi.Point2f(dr.sin(angle_shift), -dr.cos(angle_shift)) direction1 = to_world_direction(direction1, direction) direction2 = to_world_direction(direction2, direction) point1 = mi.Point2f(dr.select(active, origin + radius * direction1, origin)) point2 = mi.Point2f(dr.select(active, origin + radius * direction2, origin)) return point1, point2, dr.cos(angle_shift) / (2 * radius) , 2 def pdf_cosine_boundary_(sampled_direction, R, direction): return 1/4 * dr.abs(dr.dot(dr.normalize(sampled_direction), dr.normalize(direction))) / R def pdf_cosine_boundary(points, origin, R, direction): d = dr.normalize(points - origin) return pdf_cosine_boundary_(d, R, direction) def sample_uniform_volume(sample, origin, radius): r = radius * dr.sqrt(sample[0]) theta = 2 * dr.pi * sample[1] return mi.Point2f(origin + r * mi.Point2f(dr.cos(theta),dr.sin(theta))), dr.rcp(dr.pi * dr.sqr(radius)) def sample_sec_direction(sample : Float, direction : mi.Point2f, threshold : Float = Float(0.49 * dr.pi)): negative = sample >= 0.5 sample = dr.select(negative, 2 * sample - 1, 2 * sample) angle_shift = sample_sec_angle(sample, threshold) angle_shift *= dr.select(negative, -1., 1) angle_initial = dr.atan2(direction[1], direction[0]) angle = angle_initial + angle_shift sampled_direction = mi.Point2f(dr.cos(angle), dr.sin(angle)) return sampled_direction @dr.syntax def pdf_sec_direction(dir : mi.Point2f, direction : mi.Point2f, threshold : Float = Float(0.49 * dr.pi)): pdf = Float(0) sec = dr.rcp(dr.dot(dir, direction)) csc_d = dr.rcp(dr.sin(threshold)) sec_d = dr.rcp(dr.cos(threshold)) normalization = 0.5 * dr.log((1 + csc_d)/(-1 + csc_d)) + (dr.pi/2 - threshold) * sec_d if (sec > 0) & (sec < sec_d): pdf = sec elif (sec >= sec_d): pdf = sec_d return pdf / normalization * 0.5 @dr.syntax def sample_sec_angle(sample : Float, threshold : Float = Float(0.49 * dr.pi)): csc_d = dr.rcp(dr.sin(threshold)) sec_d = dr.rcp(dr.cos(threshold)) th_val = 0.5 * dr.log((1 + csc_d)/(-1 + csc_d)) normalization = th_val + (dr.pi/2 - threshold) * sec_d sample *= normalization sampled_p = Float(0) if sample < th_val: exp = dr.exp(2 * sample) sampled_p = dr.asin((exp - 1)/(exp + 1)) else: sampled_p = threshold + (sample - th_val) / (normalization - th_val) * (dr.pi / 2 - threshold) return sampled_p @dr.syntax def pdf_sec_angle(angle : Float, threshold : Float = Float(0.49 * dr.pi)): # pdf with respect to secant. pdf = Float(0) sec = dr.rcp(dr.cos(angle)) csc_d = dr.rcp(dr.sin(threshold)) sec_d = dr.rcp(dr.cos(threshold)) normalization = 0.5 * dr.log((1 + csc_d)/(-1 + csc_d)) + (dr.pi/2 - threshold) * sec_d if (angle >= 0) & (angle < threshold): pdf = sec elif (angle >= threshold) & (angle <= dr.pi/2): pdf = sec_d return pdf / normalization @dr.syntax def eval_dP_norm(radius : Float, σ : Float) -> Float: # used in directional derivative sqrtσ = dr.sqrt(σ) z = radius * sqrtσ result = Float(0) if z < 0.001: result = dr.rcp(dr.pi * dr.square(radius)) else: result = sqrtσ * dr.rcp(2 * dr.pi * radius * i1(radius * sqrtσ)) return result def eval_Pσr_(r, R, sigma, in_mask = Bool(False)): # multiplied with 2 * pi * r version z = R * dr.sqrt(sigma) y = r / R return dr.select(in_mask, Qσ(y, z), eval_Pσrs_(R, sigma)) def eval_Pσrs_(R, sigma): return dr.rcp(i0(R * dr.sqrt(sigma)))