python - Rotating a Bitmap with 3 Shears

Question

I am rotating a bitmap using the the three shear method documented in these articles [1][2].

From about 0-90°, the quality is acceptable, but beyond that it gets progressively more distorted until it's unintelligible.

Can anyone help me locate what is going wrong? There are a few calls to methods from the application Cinema 4D's API, but I believe the issue is coming from the math. Thank you!

This is my shear function:

def shear(angle,x,y):
    '''
    |1  -tan(??/2) |  |1        0|  |1  -tan(??/2) |
    |0      1     |  |sin(??)   1|  |0      1     |

    '''
    # shear 1
    tangent=math.tan(angle/2)
    new_x=round(x-y*tangent)
    new_y=y

    #shear 2
    new_y=round(new_x*math.sin(angle)+new_y)      #since there is no change in new_x according to the shear matrix

    #shear 3
    new_x=round(new_x-new_y*tangent)              #since there is no change in new_y according to the shear matrix

    return new_x,new_y

This is the code in the draw function:

cos = math.cos(self.rotation)
sin = math.sin(self.rotation)

# Define the width and height of the destination image
newWidth = round(abs(w*cos)+abs(h*sin))+1
newHeight = round(abs(h*cos)+abs(w*sin))+1

destBmp = c4d.bitmaps.BaseBitmap() #creates a new BaseBitmap instance for the destination image
destBmp.Init(newWidth,newHeight) #initializes the bitmap
destAlpha = destBmp.AddChannel(True, False) #adds an alpha channel

# Find the center of the source image for rotation
origCenterWidth  = round(((w+1)/2)-1)    #with respect to the source image
origCenterHeight = round(((h+1)/2)-1)    #with respect to the source image

# Find the center of the destination image
newCenterWidth  = round(((newWidth+1)/2)-1)  #with respect to the destination image
newCenterHeight = round(((newHeight)/2)-1)  #with respect to the destination image

for xP in range(w):
  for yP in range(h):
      destBmp.SetPixel(int(xP), int(yP), 0, 0, 255) #sets the destination bitmap's background color to blue

for i in range(h):
    for j in range(w):
        #co-ordinates of pixel with respect to the center of source image
        x = w-1-j-origCenterWidth
        y = h-1-i-origCenterHeight

        #Applying the Shear Transformation
        new_x,new_y = shear(self.rotation,x,y)

        #with rotation, the center will change so new_x and new_y will be the new center
        new_y = newCenterHeight-new_y
        new_x = newCenterWidth-new_x

        alphaValue = sourceBmp.GetAlphaPixel(alphaChannel, j, i) #gets the source image pixel's alpha
        col = sourceBmp.GetPixelDirect(j, i) #gets the source image pixel's color as a Color Vector
        destBmp.SetAlphaPixel(nBmpAlpha, int(new_x), int(new_y), alphaValue) #sets the destination image pixel's alpha
        destBmp.SetPixel(int(new_x), int(new_y), int(col.x), int(col.y), int(col.z)) #sets the destination image pixel's color

question from:https://stackoverflow.com/questions/65909025/rotating-a-bitmap-with-3-shears

Answer 1

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