geom: add simple frustum class

CMakeLists.txt

@@ -205,6 +205,8 @@ list (
     geom/cylinder.hpp
     geom/ellipse.cpp
     geom/ellipse.hpp
+    geom/frustum.cpp
+    geom/frustum.hpp
     geom/iostream.cpp
     geom/iostream.hpp
     geom/ops.hpp
@@ -450,6 +452,7 @@ if (TESTS)
         format
         geom/aabb
         geom/ray
+        geom/frustum
         hash/checksum
         hash/crc
         hash/fasthash

geom/frustum.cpp

@@ -0,0 +1,68 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2018 Danny Robson <danny@nerdcruft.net>
+ */
+
+#include "frustum.hpp"
+
+using util::geom::frustum;
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
+frustum<T>::frustum (const matrix4<T> &transform)
+{
+    // left
+    planes[0].coefficients[0] = transform[3][0] + transform[0][0];
+    planes[0].coefficients[1] = transform[3][1] + transform[0][1];
+    planes[0].coefficients[2] = transform[3][2] + transform[0][2];
+    planes[0].coefficients[3] = transform[3][3] + transform[0][3];
+
+    // Right clipping plane
+    planes[1].coefficients[0] = transform[3][0] - transform[0][0];
+    planes[1].coefficients[1] = transform[3][1] - transform[0][1];
+    planes[1].coefficients[2] = transform[3][2] - transform[0][2];
+    planes[1].coefficients[3] = transform[3][3] - transform[0][3];
+
+    // Top clipping plane
+    planes[2].coefficients[0] = transform[3][0] - transform[1][0];
+    planes[2].coefficients[1] = transform[3][1] - transform[1][1];
+    planes[2].coefficients[2] = transform[3][2] - transform[1][2];
+    planes[2].coefficients[3] = transform[3][3] - transform[1][3];
+
+    // Bottom clipping plane
+    planes[3].coefficients[0] = transform[3][0] + transform[1][0];
+    planes[3].coefficients[1] = transform[3][1] + transform[1][1];
+    planes[3].coefficients[2] = transform[3][2] + transform[1][2];
+    planes[3].coefficients[3] = transform[3][3] + transform[1][3];
+
+    // Near clipping plane
+    planes[4].coefficients[0] = transform[3][0] + transform[2][0];
+    planes[4].coefficients[1] = transform[3][1] + transform[2][1];
+    planes[4].coefficients[2] = transform[3][2] + transform[2][2];
+    planes[4].coefficients[3] = transform[3][3] + transform[2][3];
+
+    // Far clipping plane
+    planes[5].coefficients[0] = transform[3][0] - transform[2][0];
+    planes[5].coefficients[1] = transform[3][1] - transform[2][1];
+    planes[5].coefficients[2] = transform[3][2] - transform[2][2];
+    planes[5].coefficients[3] = transform[3][3] - transform[2][3];
+
+    for (auto &p: planes)
+        p = normalised (p);
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+template struct util::geom::frustum<float>;

geom/frustum.hpp

@@ -0,0 +1,68 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2018 Danny Robson <danny@nerdcruft.net>
+ */
+
+#ifndef CRUFT_UTIL_GEOM_FRUSTUM_HPP
+#define CRUFT_UTIL_GEOM_FRUSTUM_HPP
+
+#include "../matrix.hpp"
+#include "plane.hpp"
+#include "aabb.hpp"
+
+#include <array>
+
+#include <cstddef>
+
+namespace util::geom {
+    /// a viewing frustrum comprised of 4 axis planes, a near plane, and a far
+    /// plane. it may describe something other than a perspective projection
+    /// (eg, an orthographic projection)
+    template <typename ValueT>
+    struct frustum {
+        explicit frustum (const matrix<4,4,ValueT>&);
+
+        std::array<plane<3,ValueT>, 6> planes;
+    };
+
+    using frustum3f = frustum<float>;
+
+
+    /// tests whether a frustum and an aabb overlap
+    ///
+    /// XXX: there may be occasional false positives.
+    template <size_t S, typename T>
+    bool
+    intersects (const frustum<T> &f, const aabb<S,T> &b)
+    {
+        for (const auto &p: f.planes) {
+            const auto n = normal (p);
+            const auto positive = n > 0;
+
+            const auto lo = select (positive, b.lo, b.hi);
+            const auto hi = select (positive, b.hi, b.lo);
+
+            if (dot (n, lo) + p.coefficients[S] > 0)
+                return false; // OUTSIDE
+
+            if (dot (n, hi) + p.coefficients[S] >= 0)
+                return true; //INTERSECT
+        }
+
+        // INSIDE
+        return true;
+    }
+};
+
+#endif

geom/fwd.hpp

@@ -11,11 +11,11 @@
  * See the License for the specific language governing permissions and
  * limitations under the License.
  *
- * Copyright 2015 Danny Robson <danny@nerdcruft.net>
+ * Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
  */
 
-#ifndef __UTIL_GEOM_FWD_HPP
+#ifndef CRUFT__UTIL_GEOM_FWD_HPP
-#define __UTIL_GEOM_FWD_HPP
+#define CRUFT__UTIL_GEOM_FWD_HPP
 
 #include <cstdlib>
 
@@ -28,6 +28,8 @@ namespace util::geom {
     template <size_t S, typename T> struct rect;
     template <size_t S, typename T> struct cylinder;
     template <size_t S, typename T> struct tri;
+
+    template <typename T> struct frustum;
 }
 
 #endif

geom/iostream.cpp

@@ -11,12 +11,14 @@
  * See the License for the specific language governing permissions and
  * limitations under the License.
  *
- * Copyright 2015 Danny Robson <danny@nerdcruft.net>
+ * Copyright 2018 Danny Robson <danny@nerdcruft.net>
  */
 
 #include "iostream.hpp"
 
 #include "sphere.hpp"
+#include "plane.hpp"
+#include "frustum.hpp"
 #include "../coord/iostream.hpp"
 
 
@@ -32,3 +34,30 @@ util::geom::operator<< (std::ostream &os, util::geom::sphere<S,T> s)
 //-----------------------------------------------------------------------------
 template std::ostream& util::geom::operator<< (std::ostream&, util::geom::sphere<2,float>);
 template std::ostream& util::geom::operator<< (std::ostream&, util::geom::sphere<3,float>);
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <size_t S, typename T>
+std::ostream&
+util::geom::operator<< (std::ostream &os, plane<S,T> val)
+{
+    return os << val.coefficients;
+}
+
+
+//-----------------------------------------------------------------------------
+template std::ostream& util::geom::operator<< (std::ostream&, plane<2,float>);
+template std::ostream& util::geom::operator<< (std::ostream&, plane<3,float>);
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
+std::ostream&
+util::geom::operator<< (std::ostream &os, frustum<T> val)
+{
+    return os << "[ " << util::make_infix (val.planes) << " ]";
+}
+
+
+//-----------------------------------------------------------------------------
+template std::ostream& util::geom::operator<< (std::ostream&, frustum<float>);

geom/iostream.hpp

@@ -11,11 +11,11 @@
  * See the License for the specific language governing permissions and
  * limitations under the License.
  *
- * Copyright 2015-2016 Danny Robson <danny@nerdcruft.net>
+ * Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
  */
 
-#ifndef __UTIL_GEOM_IOSTREAM_HPP
+#ifndef CRUFT_UTIL_GEOM_IOSTREAM_HPP
-#define __UTIL_GEOM_IOSTREAM_HPP
+#define CRUFT_UTIL_GEOM_IOSTREAM_HPP
 
 #include "fwd.hpp"
 
@@ -35,6 +35,14 @@ namespace util::geom {
     template <size_t S, typename T>
     std::ostream&
     operator<< (std::ostream&, sphere<S,T>);
+
+    template <size_t S, typename T>
+    std::ostream&
+    operator<< (std::ostream&, plane<S,T>);
+
+    template <typename T>
+    std::ostream&
+    operator<< (std::ostream&, frustum<T>);
 }
 
 #endif

test/geom/frustum.cpp

@@ -0,0 +1,35 @@
+#include "tap.hpp"
+
+#include "geom/frustum.hpp"
+#include "geom/aabb.hpp"
+#include "matrix.hpp"
+
+#include "geom/iostream.hpp"
+#include <iostream>
+
+///////////////////////////////////////////////////////////////////////////////
+int
+main ()
+{
+    util::TAP::logger tap;
+
+    const util::geom::frustum3f origin90 (
+        util::perspective (90.f, 1.f, {0.01f, 1.f})
+    );
+
+    static const struct {
+        util::geom::aabb3f box;
+        bool intersects;
+        const char *message;
+    } TESTS[] = {
+        { { { -1, -1, -1 }, {  1,  1,  1 } }, true,  "covers origin with unit radius" },
+        { { { -9, -9, -9 }, { -8, -8, -8 } }, false, "out of view negative" },
+        { { { -1, -1,  2 }, {  1,  1,  3 } }, false, "past far plane" },
+    };
+
+    for (const auto &t: TESTS) {
+        tap.expect_eq (intersects (origin90, t.box), t.intersects, "origin frustrum, %s", t.message);
+    }
+
+    return tap.status ();
+};