Add ansatz, cmp_volume, cmp_area and cmp_length

- Added `det`, `inv`, `dyad` and `gauss_leg` procedures in the `forcad_utils` module.
- Added procedure `set1a` to the `nurbs_curve` derived type.
- Added procedure `set4` to the `nurbs_curve` NURBS derived type.
- Added optional input variable `elem` to `derivative_scalar` procedures.
- Added `ansatz` procedures to compute shape functions, derivatives of shape functions and (dV, dA, dL).
- Added `cmp_length()` to compute the length of a NURBS curve.
- Added `cmp_area()` to compute the area of a NURBS surface.
- Added `cmp_volume()` to compute the volume of a NURBS volume.
- Added examples for `cmp_length()`, `cmp_area()`, and `cmp_volume()`.

Signed-off-by: Seyed Ali Ghasemi <info@gha3mi.com>

CHANGELOG.md

@@ -4,6 +4,20 @@ All notable changes to [ForCAD](https://github.com/gha3mi/forcad) will be docume
 
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.1.0/),
 
+## [Unreleased]
+
+### Added
+
+- Added `det`, `inv`, `dyad` and `gauss_leg` procedures in the `forcad_utils` module.
+- Added procedure `set1a` to the `nurbs_curve` derived type.
+- Added procedure `set4` to the `nurbs_curve` NURBS derived type.
+- Added optional input variable `elem` to `derivative_scalar` procedures.
+- Added `ansatz` procedures to compute shape functions, derivatives of shape functions and (dV, dA, dL).
+- Added `cmp_length()` to compute the length of a NURBS curve.
+- Added `cmp_area()` to compute the area of a NURBS surface.
+- Added `cmp_volume()` to compute the volume of a NURBS volume.
+- Added examples for `cmp_length()`, `cmp_area()`, and `cmp_volume()`.
+
 ## [0.5.1]
 
 ### Changed

example/cmp_area.f90

@@ -0,0 +1,23 @@
+program compute_area
+
+    use forcad
+
+    implicit none
+
+    type(nurbs_surface) :: shape
+    real(rk) :: area
+    real(rk) :: Xc(4,3)
+
+    Xc(1,:) = [0.0_rk, 0.0_rk, 0.0_rk]
+    Xc(2,:) = [2.0_rk, 0.0_rk, 0.0_rk]
+    Xc(3,:) = [0.0_rk, 2.0_rk, 0.0_rk]
+    Xc(4,:) = [2.0_rk, 2.0_rk, 0.0_rk]
+
+    call shape%set(&
+        knot1=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        knot2=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        Xc=Xc)
+
+    call shape%cmp_area(area)
+    print*, area
+end program

example/cmp_length.f90

@@ -0,0 +1,20 @@
+program compute_length
+
+    use forcad
+
+    implicit none
+
+    type(nurbs_curve) :: shape
+    real(rk) :: length
+    real(rk) :: Xc(2,3)
+
+    Xc(1,:) = [0.0_rk, 0.0_rk, 0.0_rk]
+    Xc(2,:) = [2.0_rk, 0.0_rk, 0.0_rk]
+
+    call shape%set(&
+        knot=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        Xc=Xc)
+
+    call shape%cmp_length(length)
+    print*, length
+end program

example/cmp_volume.f90

@@ -0,0 +1,28 @@
+program compute_volume
+
+    use forcad
+
+    implicit none
+
+    type(nurbs_volume) :: shape
+    real(rk) :: volume
+    real(rk) :: Xc(8,3)
+
+    Xc(1,:) = [0.0_rk, 0.0_rk, 0.0_rk]
+    Xc(2,:) = [2.0_rk, 0.0_rk, 0.0_rk]
+    Xc(3,:) = [0.0_rk, 2.0_rk, 0.0_rk]
+    Xc(4,:) = [2.0_rk, 2.0_rk, 0.0_rk]
+    Xc(5,:) = [0.0_rk, 0.0_rk, 2.0_rk]
+    Xc(6,:) = [2.0_rk, 0.0_rk, 2.0_rk]
+    Xc(7,:) = [0.0_rk, 2.0_rk, 2.0_rk]
+    Xc(8,:) = [2.0_rk, 2.0_rk, 2.0_rk]
+
+    call shape%set(&
+        knot1=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        knot2=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        knot3=[0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk],&
+        Xc=Xc)
+
+    call shape%cmp_volume(volume)
+    print*, volume
+end program

fpm.toml

@@ -26,6 +26,7 @@ forimage    = {git="https://github.com/gha3mi/forimage.git"}
 forcolormap = {git="https://github.com/vmagnin/forcolormap.git"}
 fortime     = {git="https://github.com/gha3mi/fortime.git"}
 openmp      = "*"
+stdlib      = "*"
 
 [dev-dependencies]
 forunittest = {git="https://github.com/gha3mi/forunittest"}
@@ -158,4 +159,19 @@ main       = "nearest_point_3d.f90"
 [[example]]
 name       = "nearest_point_2d_bench"
 source-dir = "example"
-main       = "nearest_point_2d_bench.f90"
+main       = "nearest_point_2d_bench.f90"
+
+[[example]]
+name       = "cmp_length"
+source-dir = "example"
+main       = "cmp_length.f90"
+
+[[example]]
+name       = "cmp_area"
+source-dir = "example"
+main       = "cmp_area.f90"
+
+[[example]]
+name       = "cmp_volume"
+source-dir = "example"
+main       = "cmp_volume.f90"