A new post about custom 3D engine

content/posts/custom-3d-engine/bunny-1.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+T = V[F][...,:2]
+
+# Rendering
+fig = plt.figure(figsize=(6,6))
+ax = fig.add_axes([0,0,1,1], xlim=[-1,+1], ylim=[-1,+1], aspect=1, frameon=False)
+collection = PolyCollection(T, closed=True, linewidth=0.1,
+                            facecolor="None", edgecolor="black")
+ax.add_collection(collection)
+plt.savefig("bunny-1.png", dpi=300)
+plt.show()

content/posts/custom-3d-engine/bunny-2.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+
+def frustum(left, right, bottom, top, znear, zfar):
+    M = np.zeros((4, 4), dtype=np.float32)
+    M[0, 0] = +2.0 * znear / (right - left)
+    M[1, 1] = +2.0 * znear / (top - bottom)
+    M[2, 2] = -(zfar + znear) / (zfar - znear)
+    M[0, 2] = (right + left) / (right - left)
+    M[2, 1] = (top + bottom) / (top - bottom)
+    M[2, 3] = -2.0 * znear * zfar / (zfar - znear)
+    M[3, 2] = -1.0
+    return M
+
+def perspective(fovy, aspect, znear, zfar):
+    h = np.tan(0.5*np.radians(fovy)) * znear
+    w = h * aspect
+    return frustum(-w, w, -h, h, znear, zfar)
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+V = np.c_[V, np.ones(len(V))]  @ perspective(25,1,1,100).T
+V /= V[:,3].reshape(-1,1)
+T = V[F][...,:2]
+
+# Rendering
+fig = plt.figure(figsize=(6,6))
+ax = fig.add_axes([0,0,1,1], xlim=[-1,+1], ylim=[-1,+1], aspect=1, frameon=False)
+collection = PolyCollection(T, closed=True, linewidth=0.1,
+                            facecolor="None", edgecolor="black")
+ax.add_collection(collection)
+plt.savefig("bunny-2.png", dpi=300)
+plt.show()

content/posts/custom-3d-engine/bunny-3.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+
+def frustum(left, right, bottom, top, znear, zfar):
+    M = np.zeros((4, 4), dtype=np.float32)
+    M[0, 0] = +2.0 * znear / (right - left)
+    M[1, 1] = +2.0 * znear / (top - bottom)
+    M[2, 2] = -(zfar + znear) / (zfar - znear)
+    M[0, 2] = (right + left) / (right - left)
+    M[2, 1] = (top + bottom) / (top - bottom)
+    M[2, 3] = -2.0 * znear * zfar / (zfar - znear)
+    M[3, 2] = -1.0
+    return M
+
+def perspective(fovy, aspect, znear, zfar):
+    h = np.tan(0.5*np.radians(fovy)) * znear
+    w = h * aspect
+    return frustum(-w, w, -h, h, znear, zfar)
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+V += (0,0,-3.5)
+V = np.c_[V, np.ones(len(V))]  @ perspective(25,1,1,100).T
+V /= V[:,3].reshape(-1,1)
+T = V[F][...,:2]
+
+# Rendering
+fig = plt.figure(figsize=(6,6))
+ax = fig.add_axes([0,0,1,1], xlim=[-1,+1], ylim=[-1,+1], aspect=1, frameon=False)
+collection = PolyCollection(T, closed=True, linewidth=0.1,
+                            facecolor="None", edgecolor="black")
+ax.add_collection(collection)
+plt.savefig("bunny-3.png", dpi=300)
+plt.show()

content/posts/custom-3d-engine/bunny-4.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+
+def frustum(left, right, bottom, top, znear, zfar):
+    M = np.zeros((4, 4), dtype=np.float32)
+    M[0, 0] = +2.0 * znear / (right - left)
+    M[1, 1] = +2.0 * znear / (top - bottom)
+    M[2, 2] = -(zfar + znear) / (zfar - znear)
+    M[0, 2] = (right + left) / (right - left)
+    M[2, 1] = (top + bottom) / (top - bottom)
+    M[2, 3] = -2.0 * znear * zfar / (zfar - znear)
+    M[3, 2] = -1.0
+    return M
+
+def perspective(fovy, aspect, znear, zfar):
+    h = np.tan(0.5*np.radians(fovy)) * znear
+    w = h * aspect
+    return frustum(-w, w, -h, h, znear, zfar)
+def translate(x, y, z):
+    return np.array([[1, 0, 0, x],
+                     [0, 1, 0, y],
+                     [0, 0, 1, z],
+                     [0, 0, 0, 1]], dtype=float)
+
+def xrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return np.array([[1, 0,  0, 0],
+                     [0, c, -s, 0],
+                     [0, s,  c, 0],
+                     [0, 0,  0, 1]], dtype=float)
+
+def yrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return  np.array([[ c, 0, s, 0],
+                      [ 0, 1, 0, 0],
+                      [-s, 0, c, 0],
+                      [ 0, 0, 0, 1]], dtype=float)
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+
+model = xrotate(20) @ yrotate(45) 
+view  = translate(0,0,-3.5)
+proj  = perspective(25, 1, 1, 100) 
+MVP   = proj  @ view  @ model 
+
+V = np.c_[V, np.ones(len(V))]  @ MVP.T
+V /= V[:,3].reshape(-1,1)
+T = V[F][...,:2]
+
+# Rendering
+fig = plt.figure(figsize=(6,6))
+ax = fig.add_axes([0,0,1,1], xlim=[-1,+1], ylim=[-1,+1], aspect=1, frameon=False)
+collection = PolyCollection(T, closed=True, linewidth=0.1,
+                            facecolor="None", edgecolor="black")
+ax.add_collection(collection)
+plt.savefig("bunny-4.png", dpi=300)
+plt.show()

content/posts/custom-3d-engine/bunny-5.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+
+def frustum(left, right, bottom, top, znear, zfar):
+    M = np.zeros((4, 4), dtype=np.float32)
+    M[0, 0] = +2.0 * znear / (right - left)
+    M[1, 1] = +2.0 * znear / (top - bottom)
+    M[2, 2] = -(zfar + znear) / (zfar - znear)
+    M[0, 2] = (right + left) / (right - left)
+    M[2, 1] = (top + bottom) / (top - bottom)
+    M[2, 3] = -2.0 * znear * zfar / (zfar - znear)
+    M[3, 2] = -1.0
+    return M
+
+def perspective(fovy, aspect, znear, zfar):
+    h = np.tan(0.5*np.radians(fovy)) * znear
+    w = h * aspect
+    return frustum(-w, w, -h, h, znear, zfar)
+def translate(x, y, z):
+    return np.array([[1, 0, 0, x],
+                     [0, 1, 0, y],
+                     [0, 0, 1, z],
+                     [0, 0, 0, 1]], dtype=float)
+
+def xrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return np.array([[1, 0,  0, 0],
+                     [0, c, -s, 0],
+                     [0, s,  c, 0],
+                     [0, 0,  0, 1]], dtype=float)
+
+def yrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return  np.array([[ c, 0, s, 0],
+                      [ 0, 1, 0, 0],
+                      [-s, 0, c, 0],
+                      [ 0, 0, 0, 1]], dtype=float)
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+
+
+model = xrotate(20) @ yrotate(45) 
+view  = translate(0,0,-3.5)
+proj  = perspective(25, 1, 1, 100) 
+MVP   = proj  @ view  @ model 
+
+V_ = np.c_[V, np.ones(len(V))]  @ MVP.T
+V_ /= V_[:,3].reshape(-1,1)
+T = V_[F][...,:2]
+
+fig = plt.figure(figsize=(6,6))
+for i,(fovy,z) in enumerate([(25,-3), (40,-2.), (65,-1.25), (80,-1.0)]):
+    view  = translate(0,0,z)
+    proj  = perspective(fovy, 1, 1, 100) 
+    MVP   = proj  @ view  @ model 
+    V_ = np.c_[V, np.ones(len(V))]  @ MVP.T
+    V_ /= V_[:,3].reshape(-1,1)
+    T = V_[F][...,:2]
+    ax = plt.subplot(2,2,i+1, xlim=[-1,+1], ylim=[-1,+1], aspect=1)
+    ax.axis('off')
+    collection = PolyCollection(T, closed=True, linewidth=0.1,
+                                facecolor="None", edgecolor="black")
+    ax.add_collection(collection)
+    ax.set_title("Aperture: %d" % fovy)
+
+plt.tight_layout()
+plt.savefig("bunny-5.png", dpi=300)
+plt.show()

content/posts/custom-3d-engine/bunny-6.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.collections import PolyCollection
+
+
+def frustum(left, right, bottom, top, znear, zfar):
+    M = np.zeros((4, 4), dtype=np.float32)
+    M[0, 0] = +2.0 * znear / (right - left)
+    M[1, 1] = +2.0 * znear / (top - bottom)
+    M[2, 2] = -(zfar + znear) / (zfar - znear)
+    M[0, 2] = (right + left) / (right - left)
+    M[2, 1] = (top + bottom) / (top - bottom)
+    M[2, 3] = -2.0 * znear * zfar / (zfar - znear)
+    M[3, 2] = -1.0
+    return M
+
+def perspective(fovy, aspect, znear, zfar):
+    h = np.tan(0.5*np.radians(fovy)) * znear
+    w = h * aspect
+    return frustum(-w, w, -h, h, znear, zfar)
+def translate(x, y, z):
+    return np.array([[1, 0, 0, x],
+                     [0, 1, 0, y],
+                     [0, 0, 1, z],
+                     [0, 0, 0, 1]], dtype=float)
+
+def xrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return np.array([[1, 0,  0, 0],
+                     [0, c, -s, 0],
+                     [0, s,  c, 0],
+                     [0, 0,  0, 1]], dtype=float)
+
+def yrotate(theta):
+    t = np.pi * theta / 180
+    c, s = np.cos(t), np.sin(t)
+    return  np.array([[ c, 0, s, 0],
+                      [ 0, 1, 0, 0],
+                      [-s, 0, c, 0],
+                      [ 0, 0, 0, 1]], dtype=float)
+
+# Data processing
+V, F = [], []
+with open("bunny.obj") as f:
+    for line in f.readlines():
+        if line.startswith('#'):
+            continue
+        values = line.split()
+        if not values:
+            continue
+        if values[0] == 'v':
+            V.append([float(x) for x in values[1:4]])
+        elif values[0] == 'f' :
+            F.append([int(x) for x in values[1:4]])
+V, F = np.array(V), np.array(F)-1
+
+V = (V-(V.max(0)+V.min(0))/2) / max(V.max(0)-V.min(0))
+
+model = xrotate(20) @ yrotate(45) 
+view  = translate(0,0,-3.5)
+proj  = perspective(25, 1, 1, 100) 
+MVP   = proj  @ view  @ model 
+
+V = np.c_[V, np.ones(len(V))]  @ MVP.T
+V /= V[:,3].reshape(-1,1)
+T = V[F][...,:2]
+
+# Rendering
+fig = plt.figure(figsize=(6,6))
+ax = fig.add_axes([0,0,1,1], xlim=[-1,+1], ylim=[-1,+1], aspect=1, frameon=False)
+collection = PolyCollection(T, closed=True, linewidth=0.1,
+                            facecolor="0.9", edgecolor="black")
+ax.add_collection(collection)
+plt.savefig("bunny-6.png", dpi=300)
+plt.show()