add a new create() that takes r0 and extents, also use * rsqrt instead of / sqrt

Author: karimsayedre

examples_tests

@@ -59,6 +59,32 @@ struct SphericalRectangle
         return retval;
     }
 
+    // Create directly from a local-frame corner position and rectangle extents.
+    // Use when you already know r0 (e.g. from a gnomonic projection) and don't
+    // need the shapes::SphericalRectangle + solidAngle(observer) roundtrip.
+    static SphericalRectangle<T> create(const vector3_type _r0, const vector2_type _extents)
+    {
+        // Same math as shapes::SphericalRectangle::solidAngle() but without
+        // the mul(basis, origin - observer) step since we already have r0.
+        typename shapes::SphericalRectangle<T>::solid_angle_type sa;
+        sa.r0 = _r0;
+
+        const scalar_type zSq = _r0.z * _r0.z;
+        const vector4_type denorm_n_z = vector4_type(-_r0.y, _r0.x + _extents.x, _r0.y + _extents.y, -_r0.x);
+        sa.n_z = denorm_n_z * hlsl::rsqrt<vector4_type>(hlsl::promote<vector4_type>(zSq) + denorm_n_z * denorm_n_z);
+        sa.cosGamma = vector4_type(
+            -sa.n_z[0] * sa.n_z[1], -sa.n_z[1] * sa.n_z[2],
+            -sa.n_z[2] * sa.n_z[3], -sa.n_z[3] * sa.n_z[0]);
+
+        math::sincos_accumulator<scalar_type> acc = math::sincos_accumulator<scalar_type>::create(sa.cosGamma[0]);
+        acc.addCosine(sa.cosGamma[1]);
+        acc.addCosine(sa.cosGamma[2]);
+        acc.addCosine(sa.cosGamma[3]);
+        sa.value = acc.getSumOfArccos() - scalar_type(2.0) * numbers::pi<scalar_type>;
+
+        return create(sa, _extents);
+    }
+
     // shared core of generate and generateSurfaceOffset
     // returns (xu, hv, d) packed into a vector3; caller derives either 2D offset or 3D direction
     vector3_type __generate(const domain_type u) NBL_CONST_MEMBER_FUNC

include/nbl/builtin/hlsl/sampling/spherical_rectangle.hlsl

@@ -112,7 +112,7 @@ struct SphericalRectangle
         result.r0 = hlsl::mul(basis, origin - observer);
 
         const vector4_type denorm_n_z = vector4_type(-result.r0.y, result.r0.x + extents.x, result.r0.y + extents.y, -result.r0.x);
-        result.n_z = denorm_n_z / nbl::hlsl::sqrt(hlsl::promote<vector4_type>(result.r0.z * result.r0.z) + denorm_n_z * denorm_n_z);
+        result.n_z = denorm_n_z * hlsl::rsqrt<vector4_type>(hlsl::promote<vector4_type>(result.r0.z * result.r0.z) + denorm_n_z * denorm_n_z);
         result.cosGamma = vector4_type(
             -result.n_z[0] * result.n_z[1],
             -result.n_z[1] * result.n_z[2],